#include <bits/stdc++.h>

using namespace std;

#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return {i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (c it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(x...) " [" #x ": " << (x) << "] "

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
template <typename A, typename B>
using unordered_map2 = __gnu_pbds::gp_hash_table<A, B>;
using namespace __gnu_pbds;
template <typename T> using ordered_set =
  __gnu_pbds::tree<T, __gnu_pbds::null_type, less<T>, __gnu_pbds::rb_tree_tag,
                   __gnu_pbds::tree_order_statistics_node_update>;
// ordered_set<int> s; s.insert(1); s.insert(2);
// s.order_of_key(1);    // Out: 0.
// *s.find_by_order(1);  // Out: 2.

using ld = long double;
using ll = long long;

constexpr int mod = 1000 * 1000 * 1000 + 7;
constexpr int odw2 = (mod + 1) / 2;

void OdejmijOd(int& a, int b) { a -= b; if (a < 0) a += mod; }
int Odejmij(int a, int b) { OdejmijOd(a, b); return a; }
void DodajDo(int& a, int b) { a += b; if (a >= mod) a -= mod; }
int Dodaj(int a, int b) { DodajDo(a, b); return a; }
int Mnoz(int a, int b) { return (ll) a * b % mod; }
void MnozDo(int& a, int b) { a = Mnoz(a, b); }
int Pot(int a, ll b) { int res = 1; while (b) { if (b % 2 == 1) MnozDo(res, a); a = Mnoz(a, a); b /= 2; } return res; }
int Odw(int a) { return Pot(a, mod - 2); }
void PodzielDo(int& a, int b) { MnozDo(a, Odw(b)); }
int Podziel(int a, int b) { return Mnoz(a, Odw(b)); }
int Moduluj(ll x) { x %= mod; if (x < 0) x += mod; return x; }

template <typename T> T Maxi(T& a, T b) { return a = max(a, b); }
template <typename T> T Mini(T& a, T b) { return a = min(a, b); }

class BigInteger {
 // Performs binary arithmetic modulo 2**MAX_BIT.

 public:
  using Uint = uint64_t;
  using Uint2 = __uint128_t;
  static constexpr int MAX_BIT = 10'112;  // 64 * 158
  static constexpr int GROUP_SIZE = 64;
  static constexpr int MAX_GROUP = MAX_BIT / GROUP_SIZE;
  static_assert(MAX_BIT % 2 == 0);
  static_assert(MAX_BIT % GROUP_SIZE == 0);
  static_assert(GROUP_SIZE % 2 == 0);

  BigInteger() {
    fill(groups, groups + MAX_GROUP, 0);
  }

  explicit BigInteger(Uint x) : BigInteger() {
    groups[0] = x;
  }

  uint64_t GetBit(int b) const {
    assert(0 <= b and b < MAX_BIT);
    return (groups[b / GROUP_SIZE] >> (b % GROUP_SIZE)) & 1;
  }

  void SetBit(int b, uint64_t value) {
    assert(0 <= b and b < MAX_BIT);
    assert(0 <= value and value <= 1);
    value <<= (b % GROUP_SIZE);
    uint64_t& group = groups[b / GROUP_SIZE];
    group ^= value;
    value ^= group & value;
    group ^= value;
  }

  bool Increment() {
    for (int i = 0; i < MAX_GROUP; i++) {
      groups[i]++;
      if (groups[i] != 0) {
        return false;
      }
    }
    return true;
  }

  void Negate() {
    for (int i = 0; i < MAX_GROUP; i++) {
      groups[i] = ~groups[i];
    }
    Increment();
  }

  void Sub(const BigInteger& other) {
    Negate();
    Add(other);
    Negate();
  }

  bool Add(const BigInteger& other) {
    Uint carry = 0;
    for (int i = 0; i < MAX_GROUP; i++) {
      const Uint sum = groups[i] + carry;
      carry = 0;
      if (sum < groups[i]) {
        carry = 1;
      }
      const Uint sum2 = sum + other.groups[i];
      if (sum2 < sum) {
        carry = 1;
      }
      groups[i] = sum2;
    }
    return carry > 0;
  }

  bool Mul2() {
    Uint carry = 0;
    for (int i = 0; i < MAX_GROUP; i++) {
      const Uint new_carry = groups[i] >> (GROUP_SIZE - 1);
      groups[i] <<= 1;
      groups[i] |= carry;
      carry = new_carry;
    }
    return carry > 0;
  }

  void Xor(const BigInteger& other) {
    for (int i = 0; i < MAX_GROUP; i++) {
      groups[i] ^= other.groups[i];
    }
  }

  void ShiftLeft(int n) {
    const int group_shift = n / GROUP_SIZE;
    const int shift_in_group = n % 64;
    for (int i = MAX_GROUP - 1; i >= 0; i--) {
      Uint high = 0;
      if (i - group_shift >= 0) {
        high = groups[i - group_shift] << shift_in_group;
      }
      Uint low = 0;
      if (i - group_shift - 1 >= 0 and shift_in_group > 0) {
        low = groups[i - group_shift - 1] >> (GROUP_SIZE - shift_in_group);
      }
      groups[i] = high | low;
    }
  }

  void ShiftRight(int n) {
    const int group_shift = n / GROUP_SIZE;
    const int shift_in_group = n % 64;
    for (int i = 0; i < MAX_GROUP; i++) {
      Uint high = 0;
      if (i + group_shift + 1 < MAX_GROUP and shift_in_group > 0) {
        high = groups[i + group_shift + 1] << (GROUP_SIZE - shift_in_group);
      }
      Uint low = 0;
      if (i + group_shift < MAX_GROUP) {
        low = groups[i + group_shift] >> shift_in_group;
      }
      groups[i] = high | low;
    }
  }

  int GetLeadingOne() const {
    for (int i = MAX_GROUP - 1; i >= 0; i--) {
      if (groups[i]) {
        return i * GROUP_SIZE + 63 - __builtin_clzll(groups[i]);
      }
    }
    return -1;
  }

  void Mod(const BigInteger& other) {
    *this = Divide(other);
  }

  BigInteger Divide(const BigInteger& other) {
    // Divides this number by "other".
    // Returns the remainder module "other".
    static vector<BigInteger> powers;
    powers.clear();
    powers.reserve(MAX_BIT);
    powers.push_back(other);
    while (powers.back() <= *this) {
      powers.push_back(powers.back());
      powers.back().Mul2();
    }
    BigInteger result;
    for (int i = (int) powers.size() - 2; i >= 0; i--) {
      if (powers[i] <= *this) {
        Sub(powers[i]);
        result.SetBit(i, 1);
      }
    }
    swap(result, *this);
    return result;
  }

  void Mul(const BigInteger& other) {
    BigInteger total;
    BigInteger high;
    BigInteger low;
    for (int i = 0; i < MAX_GROUP; i++) {
      high = BigInteger();
      low = BigInteger();
      const Uint2 x = groups[i];
      for (int j = 0; i + j < MAX_GROUP; j++) {
        const Uint2 product = x * other.groups[j];
        if (i + j + 1 < MAX_GROUP) {
          high.groups[i + j + 1] = (product >> GROUP_SIZE);
        }
        low.groups[i + j] = product;
      }
      total.Add(high);
      total.Add(low);
    }
    *this = total;
  }

  bool operator<(const BigInteger& other) const {
    for (int i = MAX_GROUP - 1; i >= 0; i--) {
      if (groups[i] != other.groups[i]) {
        return groups[i] < other.groups[i];
      }
    }
    return false;
  }

  bool operator<=(const BigInteger& other) const {
    return !(other < *this);
  }

  bool operator>(const BigInteger& other) const {
    return other < *this;
  }

  bool operator>=(const BigInteger& other) const {
    return other <= *this;
  }

  bool operator==(const BigInteger& other) const {
    for (int i = 0; i < MAX_GROUP; i++) {
      if (groups[i] != other.groups[i]) {
        return false;
      }
    }
    return true;
  }

  bool operator!=(const BigInteger& other) const {
    return !(*this == other);
  }

  bool IsZero() const {
    for (int i = 0; i < MAX_GROUP; i++) {
      if (groups[i] != 0) {
        return false;
      }
    }
    return true;
  }

  friend ostream& operator<<(ostream& deb, const BigInteger& i) {
    int pos = BigInteger::MAX_BIT - 1;
    while (pos > 0 and i.GetBit(pos) == 0) {
      pos--;
    }
    while (pos >= 0) {
      deb << i.GetBit(pos--);
    }
    return deb;
  }

 private:
  Uint groups[MAX_GROUP];
};

debug& operator<<(debug& deb, const BigInteger& i) {
  #ifdef LOCAL
  int pos = BigInteger::MAX_BIT - 1;
  while (pos > 0 and i.GetBit(pos) == 0) {
    pos--;
  }
  while (pos >= 0) {
    deb << i.GetBit(pos--);
  }
  #endif
  return deb;
}

class ExtendedGcd {
 public:
  // Computes (x, y) such that x * a + y * b = GCD(a, b).
  void Run(const BigInteger& a, const BigInteger& b, const BigInteger& modulo) {
    stack.emplace_back(a, b, BigInteger());
    ExpandStack();
    gcd = stack.back().b;
    UnwindStack(modulo);
  }

  const BigInteger& GetGcd() const {
    return gcd;
  }

  const BigInteger& GetX() const {
    return x;
  }

  const BigInteger& GetY() const {
    return y;
  }

 private:
  void ExpandStack() {
    while (!stack.back().a.IsZero()) {
      StackEntry& last = stack.back();
      last.floor_b_div_a = last.b;
      BigInteger remainder = last.floor_b_div_a.Divide(last.a);
      stack.emplace_back(remainder, last.a, BigInteger());
    }
  }

  void UnwindStack(const BigInteger& modulo) {
    x = BigInteger();
    y = BigInteger(1);
    stack.pop_back();
    while (!stack.empty()) {
      StackEntry& entry = stack.back();
      BigInteger& total = entry.floor_b_div_a;
      total.Mul(x);
      total.Mod(modulo);
      if (y >= total) {
        y.Sub(total);
      } else {
        y.Add(modulo);
        y.Sub(total);
      }
      swap(x, y);
      stack.pop_back();
    }
  }

  struct StackEntry {
    BigInteger a;
    BigInteger b;
    BigInteger floor_b_div_a;
  };

  vector<StackEntry> stack;
  BigInteger gcd;
  BigInteger x;
  BigInteger y;
};


// log(2) = 0 . 693 147 180 559
constexpr ll log_2 =   693'147'180'559;
// log(3) = 1 . 098 612 288 668
constexpr ll log_3 = 1'098'612'288'668;
constexpr ll log_denom = 1'000'000'000'000;

constexpr int MAX_N = 5'000;
constexpr ll ENTROPY_THRESHOLD = (log_2 + 1) * MAX_N;
constexpr int MAX_POWER_2 = ENTROPY_THRESHOLD / log_2 + 10;
constexpr int MAX_POWER_3 = ENTROPY_THRESHOLD / log_3 + 10;

class SecretGenerator {
 public:
  SecretGenerator(int n_, bool enabled_)
    : n(n_)
    , enabled(enabled_)
    , rng(0x0F5442CC7F8151A7) {}

  BigInteger GetSecret() {
    BigInteger result;
    if (enabled) {
      auto dist = uniform_int_distribution<int>(0, 1);
      auto skip_dist = uniform_int_distribution<int>(0, 10);
      for (int i = 0; i < n; i++) {
        for (int j = skip_dist(rng); j >= 0; j--) {
          dist(rng);
        }
        result.SetBit(i, dist(rng));
      }
    }
    return result;
  }

 private:
  int n;
  bool enabled;
  mt19937_64 rng;
};

class Preprocessing {
 public:
  void Run() {
    powers_of_2.reserve(MAX_POWER_2);
    powers_of_2.push_back(BigInteger(1));
    for (int i = 1; i < MAX_POWER_2; i++) {
      powers_of_2.push_back(powers_of_2.back());
      powers_of_2.back().Mul2();
    }

    powers_of_3.reserve(MAX_POWER_3);
    powers_of_3.push_back(BigInteger(1));
    for (int i = 1; i < MAX_POWER_3; i++) {
      powers_of_3.push_back(powers_of_3.back());
      powers_of_3.back().Mul2();
      powers_of_3.back().Add(powers_of_3[i - 1]);
    }
  }

  const BigInteger& GetPowerOf2(int p) const {
    assert(0 <= p and p < MAX_POWER_2);
    return powers_of_2[p];
  }

  const BigInteger& GetPowerOf3(int p) const {
    assert(0 <= p and p < MAX_POWER_3);
    return powers_of_3[p];
  }

 private:
  vector<BigInteger> powers_of_2;
  vector<BigInteger> powers_of_3;
};

class MyNumber {
 public:
  explicit MyNumber(int n_)
    : n(n_)
    , number()
    , taken_2(0)
    , taken_3(0)
    , digits_2(MAX_POWER_2, 0)
    , digits_3(MAX_POWER_3, 0) {}

  void Read(const BigInteger& secret) {
    assert(n <= (int) digits_2.size());
    string s;
    cin >> s;
    assert((int) s.size() == n);
    for (int i = 0; i < n; i++) {
      if (s[i] == '0') {
        number.SetBit(n - 1 - i, 0);
      } else if (s[i] == '1') {
        number.SetBit(n - 1 - i, 1);
      } else {
        assert(false);
      }
    }
    number.Xor(secret);
    debug() << imie(number);
  }

  void Preprocess(const Preprocessing& preprocessing) {
    BigInteger tmp = number;
    for (int i = 0; i < MAX_POWER_2; i++) {
      digits_2[i] = number.GetBit(i);
    }
    for (int i = MAX_POWER_3 - 1; i >= 0; i--) {
      const BigInteger& p = preprocessing.GetPowerOf3(i);
      while (tmp >= p) {
        digits_3[i]++;
        tmp.Sub(p);
      }
      assert(0 <= digits_3[i] and digits_3[i] <= 2);
    }
    assert(tmp.IsZero());
    taken_2 = 0;
    taken_3 = 0;
    #ifdef LOCAL
    /*
    debug() << "MyData{";
    debug() << "  " imie(number);
    debug() << "  " imie(digits_2);
    debug() << "  " imie(digits_3);
    debug() << "}";
    */
    #endif
  }

  int TakeDigit2() {
    return digits_2[taken_2++];
  }

  int TakeDigit3() {
    if (!pushed_digits_3.empty()) {
      const int result = pushed_digits_3.back();
      pushed_digits_3.pop_back();
      return result;
    }
    return digits_3[taken_3++];
  }

  void PushDigit3(int digit) {
    assert(0 <= digit and digit <= 2);
    assert(pushed_digits_3.empty());
    pushed_digits_3.push_back(digit);
  }

  ll SharedEntropy() const {
    if (!pushed_digits_3.empty()) {
      return (taken_2 - 2) * log_2 + taken_3 * log_3;
    }
    return taken_2 * log_2 + taken_3 * log_3;
  }

 private:
  int n;
  BigInteger number;
  int taken_2;
  int taken_3;
  vector<int> digits_2;
  vector<int> digits_3;
  vector<int> pushed_digits_3;
};

class TheirNumber {
 public:
  TheirNumber(int n_, const Preprocessing& preprocessing_)
    : n(n_)
    , preprocessing(preprocessing_)
    , next_weird_digit_3(false)
    , digs_2(0)
    , value_2()
    , digs_3(0)
    , value_3() {}

  void PrepareForWeirdDigit3() {
    assert(!next_weird_digit_3);
    next_weird_digit_3 = true;
  }

  void NewDigit3(int digit) {
    assert(0 <= digit and digit < 3);
    if (next_weird_digit_3) {
      next_weird_digit_3 = false;
      NewDigit2(digit % 2);
      NewDigit2(digit / 2);
      return;
    }
    for (int i = 0; i < digit; i++) {
      value_3.Add(preprocessing.GetPowerOf3(digs_3));
    }
    digs_3++;
  }

  void NewDigit2(int digit) {
    assert(0 <= digit and digit < 2);
    if (digit) {
      value_2.Add(preprocessing.GetPowerOf2(digs_2));
    }
    digs_2++;
  }

  ll GatheredEntropy() const {
    return digs_2 * log_2 + digs_3 * log_3;
  }

  BigInteger RecoverNumber(const BigInteger& secret) {
    //cerr << imie(digs_2) imie(digs_3) << endl;

    assert(GatheredEntropy() >= ENTROPY_THRESHOLD);
    const BigInteger& p2 = preprocessing.GetPowerOf2(digs_2);
    const BigInteger& p3 = preprocessing.GetPowerOf3(digs_3);
    BigInteger modulo = p2;
    modulo.Mul(p3);
    assert(modulo >= preprocessing.GetPowerOf2(n));

    ExtendedGcd egcd;
    egcd.Run(p2, p3, modulo);
    assert(egcd.GetGcd() == BigInteger(1));

    BigInteger r2 = p3;
    r2.Mul(egcd.GetY());
    r2.Mod(modulo);

    BigInteger r3 = p2;
    r3.Mul(egcd.GetX());
    r3.Mod(modulo);

    BigInteger v2 = value_2;
    v2.Mul(r2);
    v2.Mod(modulo);

    BigInteger v3 = value_3;
    v3.Mul(r3);
    v3.Mod(modulo);

    BigInteger total = v2;
    total.Add(v3);
    if (total >= modulo) {
      total.Sub(modulo);
    }

    total.Xor(secret);
    return total;
  }

 private:
  int n;
  const Preprocessing& preprocessing;
  bool next_weird_digit_3;
  int digs_2;
  BigInteger value_2;
  int digs_3;
  BigInteger value_3;
};

enum class AgentType {
  ALGOSIA,
  BAJTEK,
};

enum class Move {
  PAPIER,
  KAMIEN,
  NOZYCE,
};

Move MoveFromChar(char c) {
  if (c == 'P') {
    return Move::PAPIER;
  }
  if (c == 'K') {
    return Move::KAMIEN;
  }
  if (c == 'N') {
    return Move::NOZYCE;
  }
  assert(false);
}

Move MoveFromDigit(int digit) {
  if (digit == 0) {
    return Move::PAPIER;
  }
  if (digit == 1) {
    return Move::KAMIEN;
  }
  if (digit == 2) {
    return Move::NOZYCE;
  }
  assert(false);
}

char MoveToChar(Move move) {
  for (char c : {'P', 'K', 'N'}) {
    if (MoveFromChar(c) == move) {
      return c;
    }
  }
  assert(false);
}

int MoveToDigit(Move move) {
  for (int digit = 0; digit < 3; digit++) {
    if (MoveFromDigit(digit) == move) {
      return digit;
    }
  }
  assert(false);
}

int ScoreGame(Move move_neg, Move move_pos) {
  // Returns -1 if move_neg wins, 1 if move_pos wins, 0 if draw.
  if (move_neg == move_pos) {
    return 0;
  }
  const int digit_neg = MoveToDigit(move_neg);
  const int digit_pos = MoveToDigit(move_pos);
  if ((digit_neg + 1) % 3 == digit_pos) {
    return -1;
  }
  return 1;
}

class Agent {
 public:
  Agent(
    AgentType agent_type_,
    int n_,
    const Preprocessing& preprocessing_,
    SecretGenerator& secret_generator_
  ) : n(n_)
    , agent_type(agent_type_)
    , preprocessing(preprocessing_)
    , secret_generator(secret_generator_)
    , my_number(n_)
    , their_number(n_, preprocessing_) {}

  void Run() {
    BigInteger secret = secret_generator.GetSecret();
    debug() << imie(secret);
    my_number.Read(secret);
    my_number.Preprocess(preprocessing);
    while (my_number.SharedEntropy() < ENTROPY_THRESHOLD or their_number.GatheredEntropy() < ENTROPY_THRESHOLD) {
      RunFromTieToTie();
    }
    const BigInteger result = their_number.RecoverNumber(secret);
    debug() << imie(result);
    cout << "! ";
    for (int i = n - 1; i >= 0; i--) {
      cout << result.GetBit(i);
    }
    cout << endl;
  }

 private:
  void RunFromTieToTie() {
    const Move my_move = MoveFromDigit(my_number.TakeDigit3());
    cout << MoveToChar(my_move) << endl;
    const Move their_move = ReadTheirMove();
    their_number.NewDigit3(MoveToDigit(their_move));
    const int score = ScoreGame(their_move, my_move);
    if (score == 0) {
      // Still tie.
      return;
    }
    if (score == -1) {
      // I lost.
      return RunFromImbalanceToTie(false);
    }
    if (score == 1) {
      // I won.
      return RunFromImbalanceToTie(true);
    }
    assert(false);
  }

  void RunFromImbalanceToTie(const bool am_i_winning) {
    while (true) {
      const bool should_i_share = ShouldIShare();

      Move my_move;
      if (should_i_share) {
        // Move::PAPIER or Move::KAMIEN
        const int d0 = my_number.TakeDigit2();
        const int d1 = my_number.TakeDigit2();
        if (d0 == 1 and d1 == 1) {
          if (am_i_winning) {
            my_move = Move::PAPIER;
          } else {
            my_move = Move::KAMIEN;
          }
        } else {
          my_number.PushDigit3(d1 * 2 + d0);
          if (am_i_winning) {
            my_move = Move::KAMIEN;
          } else {
            my_move = Move::PAPIER;
          }
        }
      } else if (am_i_winning) {
        my_move = Move::KAMIEN;
      } else {
        my_move = Move::PAPIER;
      }

      cout << MoveToChar(my_move) << endl;
      const Move their_move = ReadTheirMove();
      const int score = ScoreGame(their_move, my_move);

      if (!should_i_share) {
        if (score == 0) {
          their_number.NewDigit2(1);
          their_number.NewDigit2(1);
        } else {
          their_number.PrepareForWeirdDigit3();
        }
      } else if (am_i_winning) {
        assert(their_move == Move::PAPIER);
      } else {
        assert(their_move == Move::KAMIEN);
      }

      if (score == 0) {
        // Nothing changes.
        continue;
      }
      if (score == 1) {
        assert(!am_i_winning);
        // Back to tie.
        return;
      }
      if (score == -1) {
        assert(am_i_winning);
        // Back to tie.
        return;
      }
      assert(false);
    }
  }

  bool ShouldIShare() const {
    const ll shared_entropy = my_number.SharedEntropy();
    const ll gathered_entropy = their_number.GatheredEntropy();
    if (shared_entropy == gathered_entropy) {
      // Doesn't matter, resolve to Algosia.
      return agent_type == AgentType::ALGOSIA;
    }
    if (shared_entropy < gathered_entropy) {
      // I shared less than I gathered, I need to share now.
      return true;
    }
    // I shared more than I gathered, I need to gather now.
    return false;
  }

  Move ReadTheirMove() {
    char c;
    cin >> c;
    return MoveFromChar(c);
  }

  int n;
  AgentType agent_type;
  const Preprocessing& preprocessing;
  SecretGenerator& secret_generator;

  MyNumber my_number;
  TheirNumber their_number;
};

AgentType ReadAgentType() {
  string who;
  cin >> who;
  if (who == "Algosia") {
    return AgentType::ALGOSIA;
  }
  if (who == "Bajtek") {
    return AgentType::BAJTEK;
  }
  assert(false);
}

int ReadInt() {
  int n;
  cin >> n;
  return n;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);

  Preprocessing preprocessing;
  preprocessing.Run();

  const AgentType agent_type = ReadAgentType();

  const int n = ReadInt();
  const int t = ReadInt();

  SecretGenerator secret_generator(n, true);

  for (int i = 0; i < t; i++) {
    Agent agent(agent_type, n, preprocessing, secret_generator);
    agent.Run();
  }
  return 0;
}

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892

#include <bits/stdc++.h>

using namespace std;

#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return {i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (c it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(x...) " [" #x ": " << (x) << "] "

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
template <typename A, typename B>
using unordered_map2 = __gnu_pbds::gp_hash_table<A, B>;
using namespace __gnu_pbds;
template <typename T> using ordered_set =
  __gnu_pbds::tree<T, __gnu_pbds::null_type, less<T>, __gnu_pbds::rb_tree_tag,
                   __gnu_pbds::tree_order_statistics_node_update>;
// ordered_set<int> s; s.insert(1); s.insert(2);
// s.order_of_key(1);    // Out: 0.
// *s.find_by_order(1);  // Out: 2.

using ld = long double;
using ll = long long;

constexpr int mod = 1000 * 1000 * 1000 + 7;
constexpr int odw2 = (mod + 1) / 2;

void OdejmijOd(int& a, int b) { a -= b; if (a < 0) a += mod; }
int Odejmij(int a, int b) { OdejmijOd(a, b); return a; }
void DodajDo(int& a, int b) { a += b; if (a >= mod) a -= mod; }
int Dodaj(int a, int b) { DodajDo(a, b); return a; }
int Mnoz(int a, int b) { return (ll) a * b % mod; }
void MnozDo(int& a, int b) { a = Mnoz(a, b); }
int Pot(int a, ll b) { int res = 1; while (b) { if (b % 2 == 1) MnozDo(res, a); a = Mnoz(a, a); b /= 2; } return res; }
int Odw(int a) { return Pot(a, mod - 2); }
void PodzielDo(int& a, int b) { MnozDo(a, Odw(b)); }
int Podziel(int a, int b) { return Mnoz(a, Odw(b)); }
int Moduluj(ll x) { x %= mod; if (x < 0) x += mod; return x; }

template <typename T> T Maxi(T& a, T b) { return a = max(a, b); }
template <typename T> T Mini(T& a, T b) { return a = min(a, b); }

class BigInteger {
 // Performs binary arithmetic modulo 2**MAX_BIT.

 public:
  using Uint = uint64_t;
  using Uint2 = __uint128_t;
  static constexpr int MAX_BIT = 10'112;  // 64 * 158
  static constexpr int GROUP_SIZE = 64;
  static constexpr int MAX_GROUP = MAX_BIT / GROUP_SIZE;
  static_assert(MAX_BIT % 2 == 0);
  static_assert(MAX_BIT % GROUP_SIZE == 0);
  static_assert(GROUP_SIZE % 2 == 0);

  BigInteger() {
    fill(groups, groups + MAX_GROUP, 0);
  }

  explicit BigInteger(Uint x) : BigInteger() {
    groups[0] = x;
  }

  uint64_t GetBit(int b) const {
    assert(0 <= b and b < MAX_BIT);
    return (groups[b / GROUP_SIZE] >> (b % GROUP_SIZE)) & 1;
  }

  void SetBit(int b, uint64_t value) {
    assert(0 <= b and b < MAX_BIT);
    assert(0 <= value and value <= 1);
    value <<= (b % GROUP_SIZE);
    uint64_t& group = groups[b / GROUP_SIZE];
    group ^= value;
    value ^= group & value;
    group ^= value;
  }

  bool Increment() {
    for (int i = 0; i < MAX_GROUP; i++) {
      groups[i]++;
      if (groups[i] != 0) {
        return false;
      }
    }
    return true;
  }

  void Negate() {
    for (int i = 0; i < MAX_GROUP; i++) {
      groups[i] = ~groups[i];
    }
    Increment();
  }

  void Sub(const BigInteger& other) {
    Negate();
    Add(other);
    Negate();
  }

  bool Add(const BigInteger& other) {
    Uint carry = 0;
    for (int i = 0; i < MAX_GROUP; i++) {
      const Uint sum = groups[i] + carry;
      carry = 0;
      if (sum < groups[i]) {
        carry = 1;
      }
      const Uint sum2 = sum + other.groups[i];
      if (sum2 < sum) {
        carry = 1;
      }
      groups[i] = sum2;
    }
    return carry > 0;
  }

  bool Mul2() {
    Uint carry = 0;
    for (int i = 0; i < MAX_GROUP; i++) {
      const Uint new_carry = groups[i] >> (GROUP_SIZE - 1);
      groups[i] <<= 1;
      groups[i] |= carry;
      carry = new_carry;
    }
    return carry > 0;
  }

  void Xor(const BigInteger& other) {
    for (int i = 0; i < MAX_GROUP; i++) {
      groups[i] ^= other.groups[i];
    }
  }

  void ShiftLeft(int n) {
    const int group_shift = n / GROUP_SIZE;
    const int shift_in_group = n % 64;
    for (int i = MAX_GROUP - 1; i >= 0; i--) {
      Uint high = 0;
      if (i - group_shift >= 0) {
        high = groups[i - group_shift] << shift_in_group;
      }
      Uint low = 0;
      if (i - group_shift - 1 >= 0 and shift_in_group > 0) {
        low = groups[i - group_shift - 1] >> (GROUP_SIZE - shift_in_group);
      }
      groups[i] = high | low;
    }
  }

  void ShiftRight(int n) {
    const int group_shift = n / GROUP_SIZE;
    const int shift_in_group = n % 64;
    for (int i = 0; i < MAX_GROUP; i++) {
      Uint high = 0;
      if (i + group_shift + 1 < MAX_GROUP and shift_in_group > 0) {
        high = groups[i + group_shift + 1] << (GROUP_SIZE - shift_in_group);
      }
      Uint low = 0;
      if (i + group_shift < MAX_GROUP) {
        low = groups[i + group_shift] >> shift_in_group;
      }
      groups[i] = high | low;
    }
  }

  int GetLeadingOne() const {
    for (int i = MAX_GROUP - 1; i >= 0; i--) {
      if (groups[i]) {
        return i * GROUP_SIZE + 63 - __builtin_clzll(groups[i]);
      }
    }
    return -1;
  }

  void Mod(const BigInteger& other) {
    *this = Divide(other);
  }

  BigInteger Divide(const BigInteger& other) {
    // Divides this number by "other".
    // Returns the remainder module "other".
    static vector<BigInteger> powers;
    powers.clear();
    powers.reserve(MAX_BIT);
    powers.push_back(other);
    while (powers.back() <= *this) {
      powers.push_back(powers.back());
      powers.back().Mul2();
    }
    BigInteger result;
    for (int i = (int) powers.size() - 2; i >= 0; i--) {
      if (powers[i] <= *this) {
        Sub(powers[i]);
        result.SetBit(i, 1);
      }
    }
    swap(result, *this);
    return result;
  }

  void Mul(const BigInteger& other) {
    BigInteger total;
    BigInteger high;
    BigInteger low;
    for (int i = 0; i < MAX_GROUP; i++) {
      high = BigInteger();
      low = BigInteger();
      const Uint2 x = groups[i];
      for (int j = 0; i + j < MAX_GROUP; j++) {
        const Uint2 product = x * other.groups[j];
        if (i + j + 1 < MAX_GROUP) {
          high.groups[i + j + 1] = (product >> GROUP_SIZE);
        }
        low.groups[i + j] = product;
      }
      total.Add(high);
      total.Add(low);
    }
    *this = total;
  }

  bool operator<(const BigInteger& other) const {
    for (int i = MAX_GROUP - 1; i >= 0; i--) {
      if (groups[i] != other.groups[i]) {
        return groups[i] < other.groups[i];
      }
    }
    return false;
  }

  bool operator<=(const BigInteger& other) const {
    return !(other < *this);
  }

  bool operator>(const BigInteger& other) const {
    return other < *this;
  }

  bool operator>=(const BigInteger& other) const {
    return other <= *this;
  }

  bool operator==(const BigInteger& other) const {
    for (int i = 0; i < MAX_GROUP; i++) {
      if (groups[i] != other.groups[i]) {
        return false;
      }
    }
    return true;
  }

  bool operator!=(const BigInteger& other) const {
    return !(*this == other);
  }

  bool IsZero() const {
    for (int i = 0; i < MAX_GROUP; i++) {
      if (groups[i] != 0) {
        return false;
      }
    }
    return true;
  }

  friend ostream& operator<<(ostream& deb, const BigInteger& i) {
    int pos = BigInteger::MAX_BIT - 1;
    while (pos > 0 and i.GetBit(pos) == 0) {
      pos--;
    }
    while (pos >= 0) {
      deb << i.GetBit(pos--);
    }
    return deb;
  }

 private:
  Uint groups[MAX_GROUP];
};

debug& operator<<(debug& deb, const BigInteger& i) {
  #ifdef LOCAL
  int pos = BigInteger::MAX_BIT - 1;
  while (pos > 0 and i.GetBit(pos) == 0) {
    pos--;
  }
  while (pos >= 0) {
    deb << i.GetBit(pos--);
  }
  #endif
  return deb;
}

class ExtendedGcd {
 public:
  // Computes (x, y) such that x * a + y * b = GCD(a, b).
  void Run(const BigInteger& a, const BigInteger& b, const BigInteger& modulo) {
    stack.emplace_back(a, b, BigInteger());
    ExpandStack();
    gcd = stack.back().b;
    UnwindStack(modulo);
  }

  const BigInteger& GetGcd() const {
    return gcd;
  }

  const BigInteger& GetX() const {
    return x;
  }

  const BigInteger& GetY() const {
    return y;
  }

 private:
  void ExpandStack() {
    while (!stack.back().a.IsZero()) {
      StackEntry& last = stack.back();
      last.floor_b_div_a = last.b;
      BigInteger remainder = last.floor_b_div_a.Divide(last.a);
      stack.emplace_back(remainder, last.a, BigInteger());
    }
  }

  void UnwindStack(const BigInteger& modulo) {
    x = BigInteger();
    y = BigInteger(1);
    stack.pop_back();
    while (!stack.empty()) {
      StackEntry& entry = stack.back();
      BigInteger& total = entry.floor_b_div_a;
      total.Mul(x);
      total.Mod(modulo);
      if (y >= total) {
        y.Sub(total);
      } else {
        y.Add(modulo);
        y.Sub(total);
      }
      swap(x, y);
      stack.pop_back();
    }
  }

  struct StackEntry {
    BigInteger a;
    BigInteger b;
    BigInteger floor_b_div_a;
  };

  vector<StackEntry> stack;
  BigInteger gcd;
  BigInteger x;
  BigInteger y;
};


// log(2) = 0 . 693 147 180 559
constexpr ll log_2 =   693'147'180'559;
// log(3) = 1 . 098 612 288 668
constexpr ll log_3 = 1'098'612'288'668;
constexpr ll log_denom = 1'000'000'000'000;

constexpr int MAX_N = 5'000;
constexpr ll ENTROPY_THRESHOLD = (log_2 + 1) * MAX_N;
constexpr int MAX_POWER_2 = ENTROPY_THRESHOLD / log_2 + 10;
constexpr int MAX_POWER_3 = ENTROPY_THRESHOLD / log_3 + 10;

class SecretGenerator {
 public:
  SecretGenerator(int n_, bool enabled_)
    : n(n_)
    , enabled(enabled_)
    , rng(0x0F5442CC7F8151A7) {}

  BigInteger GetSecret() {
    BigInteger result;
    if (enabled) {
      auto dist = uniform_int_distribution<int>(0, 1);
      auto skip_dist = uniform_int_distribution<int>(0, 10);
      for (int i = 0; i < n; i++) {
        for (int j = skip_dist(rng); j >= 0; j--) {
          dist(rng);
        }
        result.SetBit(i, dist(rng));
      }
    }
    return result;
  }

 private:
  int n;
  bool enabled;
  mt19937_64 rng;
};

class Preprocessing {
 public:
  void Run() {
    powers_of_2.reserve(MAX_POWER_2);
    powers_of_2.push_back(BigInteger(1));
    for (int i = 1; i < MAX_POWER_2; i++) {
      powers_of_2.push_back(powers_of_2.back());
      powers_of_2.back().Mul2();
    }

    powers_of_3.reserve(MAX_POWER_3);
    powers_of_3.push_back(BigInteger(1));
    for (int i = 1; i < MAX_POWER_3; i++) {
      powers_of_3.push_back(powers_of_3.back());
      powers_of_3.back().Mul2();
      powers_of_3.back().Add(powers_of_3[i - 1]);
    }
  }

  const BigInteger& GetPowerOf2(int p) const {
    assert(0 <= p and p < MAX_POWER_2);
    return powers_of_2[p];
  }

  const BigInteger& GetPowerOf3(int p) const {
    assert(0 <= p and p < MAX_POWER_3);
    return powers_of_3[p];
  }

 private:
  vector<BigInteger> powers_of_2;
  vector<BigInteger> powers_of_3;
};

class MyNumber {
 public:
  explicit MyNumber(int n_)
    : n(n_)
    , number()
    , taken_2(0)
    , taken_3(0)
    , digits_2(MAX_POWER_2, 0)
    , digits_3(MAX_POWER_3, 0) {}

  void Read(const BigInteger& secret) {
    assert(n <= (int) digits_2.size());
    string s;
    cin >> s;
    assert((int) s.size() == n);
    for (int i = 0; i < n; i++) {
      if (s[i] == '0') {
        number.SetBit(n - 1 - i, 0);
      } else if (s[i] == '1') {
        number.SetBit(n - 1 - i, 1);
      } else {
        assert(false);
      }
    }
    number.Xor(secret);
    debug() << imie(number);
  }

  void Preprocess(const Preprocessing& preprocessing) {
    BigInteger tmp = number;
    for (int i = 0; i < MAX_POWER_2; i++) {
      digits_2[i] = number.GetBit(i);
    }
    for (int i = MAX_POWER_3 - 1; i >= 0; i--) {
      const BigInteger& p = preprocessing.GetPowerOf3(i);
      while (tmp >= p) {
        digits_3[i]++;
        tmp.Sub(p);
      }
      assert(0 <= digits_3[i] and digits_3[i] <= 2);
    }
    assert(tmp.IsZero());
    taken_2 = 0;
    taken_3 = 0;
    #ifdef LOCAL
    /*
    debug() << "MyData{";
    debug() << "  " imie(number);
    debug() << "  " imie(digits_2);
    debug() << "  " imie(digits_3);
    debug() << "}";
    */
    #endif
  }

  int TakeDigit2() {
    return digits_2[taken_2++];
  }

  int TakeDigit3() {
    if (!pushed_digits_3.empty()) {
      const int result = pushed_digits_3.back();
      pushed_digits_3.pop_back();
      return result;
    }
    return digits_3[taken_3++];
  }

  void PushDigit3(int digit) {
    assert(0 <= digit and digit <= 2);
    assert(pushed_digits_3.empty());
    pushed_digits_3.push_back(digit);
  }

  ll SharedEntropy() const {
    if (!pushed_digits_3.empty()) {
      return (taken_2 - 2) * log_2 + taken_3 * log_3;
    }
    return taken_2 * log_2 + taken_3 * log_3;
  }

 private:
  int n;
  BigInteger number;
  int taken_2;
  int taken_3;
  vector<int> digits_2;
  vector<int> digits_3;
  vector<int> pushed_digits_3;
};

class TheirNumber {
 public:
  TheirNumber(int n_, const Preprocessing& preprocessing_)
    : n(n_)
    , preprocessing(preprocessing_)
    , next_weird_digit_3(false)
    , digs_2(0)
    , value_2()
    , digs_3(0)
    , value_3() {}

  void PrepareForWeirdDigit3() {
    assert(!next_weird_digit_3);
    next_weird_digit_3 = true;
  }

  void NewDigit3(int digit) {
    assert(0 <= digit and digit < 3);
    if (next_weird_digit_3) {
      next_weird_digit_3 = false;
      NewDigit2(digit % 2);
      NewDigit2(digit / 2);
      return;
    }
    for (int i = 0; i < digit; i++) {
      value_3.Add(preprocessing.GetPowerOf3(digs_3));
    }
    digs_3++;
  }

  void NewDigit2(int digit) {
    assert(0 <= digit and digit < 2);
    if (digit) {
      value_2.Add(preprocessing.GetPowerOf2(digs_2));
    }
    digs_2++;
  }

  ll GatheredEntropy() const {
    return digs_2 * log_2 + digs_3 * log_3;
  }

  BigInteger RecoverNumber(const BigInteger& secret) {
    //cerr << imie(digs_2) imie(digs_3) << endl;

    assert(GatheredEntropy() >= ENTROPY_THRESHOLD);
    const BigInteger& p2 = preprocessing.GetPowerOf2(digs_2);
    const BigInteger& p3 = preprocessing.GetPowerOf3(digs_3);
    BigInteger modulo = p2;
    modulo.Mul(p3);
    assert(modulo >= preprocessing.GetPowerOf2(n));

    ExtendedGcd egcd;
    egcd.Run(p2, p3, modulo);
    assert(egcd.GetGcd() == BigInteger(1));

    BigInteger r2 = p3;
    r2.Mul(egcd.GetY());
    r2.Mod(modulo);

    BigInteger r3 = p2;
    r3.Mul(egcd.GetX());
    r3.Mod(modulo);

    BigInteger v2 = value_2;
    v2.Mul(r2);
    v2.Mod(modulo);

    BigInteger v3 = value_3;
    v3.Mul(r3);
    v3.Mod(modulo);

    BigInteger total = v2;
    total.Add(v3);
    if (total >= modulo) {
      total.Sub(modulo);
    }

    total.Xor(secret);
    return total;
  }

 private:
  int n;
  const Preprocessing& preprocessing;
  bool next_weird_digit_3;
  int digs_2;
  BigInteger value_2;
  int digs_3;
  BigInteger value_3;
};

enum class AgentType {
  ALGOSIA,
  BAJTEK,
};

enum class Move {
  PAPIER,
  KAMIEN,
  NOZYCE,
};

Move MoveFromChar(char c) {
  if (c == 'P') {
    return Move::PAPIER;
  }
  if (c == 'K') {
    return Move::KAMIEN;
  }
  if (c == 'N') {
    return Move::NOZYCE;
  }
  assert(false);
}

Move MoveFromDigit(int digit) {
  if (digit == 0) {
    return Move::PAPIER;
  }
  if (digit == 1) {
    return Move::KAMIEN;
  }
  if (digit == 2) {
    return Move::NOZYCE;
  }
  assert(false);
}

char MoveToChar(Move move) {
  for (char c : {'P', 'K', 'N'}) {
    if (MoveFromChar(c) == move) {
      return c;
    }
  }
  assert(false);
}

int MoveToDigit(Move move) {
  for (int digit = 0; digit < 3; digit++) {
    if (MoveFromDigit(digit) == move) {
      return digit;
    }
  }
  assert(false);
}

int ScoreGame(Move move_neg, Move move_pos) {
  // Returns -1 if move_neg wins, 1 if move_pos wins, 0 if draw.
  if (move_neg == move_pos) {
    return 0;
  }
  const int digit_neg = MoveToDigit(move_neg);
  const int digit_pos = MoveToDigit(move_pos);
  if ((digit_neg + 1) % 3 == digit_pos) {
    return -1;
  }
  return 1;
}

class Agent {
 public:
  Agent(
    AgentType agent_type_,
    int n_,
    const Preprocessing& preprocessing_,
    SecretGenerator& secret_generator_
  ) : n(n_)
    , agent_type(agent_type_)
    , preprocessing(preprocessing_)
    , secret_generator(secret_generator_)
    , my_number(n_)
    , their_number(n_, preprocessing_) {}

  void Run() {
    BigInteger secret = secret_generator.GetSecret();
    debug() << imie(secret);
    my_number.Read(secret);
    my_number.Preprocess(preprocessing);
    while (my_number.SharedEntropy() < ENTROPY_THRESHOLD or their_number.GatheredEntropy() < ENTROPY_THRESHOLD) {
      RunFromTieToTie();
    }
    const BigInteger result = their_number.RecoverNumber(secret);
    debug() << imie(result);
    cout << "! ";
    for (int i = n - 1; i >= 0; i--) {
      cout << result.GetBit(i);
    }
    cout << endl;
  }

 private:
  void RunFromTieToTie() {
    const Move my_move = MoveFromDigit(my_number.TakeDigit3());
    cout << MoveToChar(my_move) << endl;
    const Move their_move = ReadTheirMove();
    their_number.NewDigit3(MoveToDigit(their_move));
    const int score = ScoreGame(their_move, my_move);
    if (score == 0) {
      // Still tie.
      return;
    }
    if (score == -1) {
      // I lost.
      return RunFromImbalanceToTie(false);
    }
    if (score == 1) {
      // I won.
      return RunFromImbalanceToTie(true);
    }
    assert(false);
  }

  void RunFromImbalanceToTie(const bool am_i_winning) {
    while (true) {
      const bool should_i_share = ShouldIShare();

      Move my_move;
      if (should_i_share) {
        // Move::PAPIER or Move::KAMIEN
        const int d0 = my_number.TakeDigit2();
        const int d1 = my_number.TakeDigit2();
        if (d0 == 1 and d1 == 1) {
          if (am_i_winning) {
            my_move = Move::PAPIER;
          } else {
            my_move = Move::KAMIEN;
          }
        } else {
          my_number.PushDigit3(d1 * 2 + d0);
          if (am_i_winning) {
            my_move = Move::KAMIEN;
          } else {
            my_move = Move::PAPIER;
          }
        }
      } else if (am_i_winning) {
        my_move = Move::KAMIEN;
      } else {
        my_move = Move::PAPIER;
      }

      cout << MoveToChar(my_move) << endl;
      const Move their_move = ReadTheirMove();
      const int score = ScoreGame(their_move, my_move);

      if (!should_i_share) {
        if (score == 0) {
          their_number.NewDigit2(1);
          their_number.NewDigit2(1);
        } else {
          their_number.PrepareForWeirdDigit3();
        }
      } else if (am_i_winning) {
        assert(their_move == Move::PAPIER);
      } else {
        assert(their_move == Move::KAMIEN);
      }

      if (score == 0) {
        // Nothing changes.
        continue;
      }
      if (score == 1) {
        assert(!am_i_winning);
        // Back to tie.
        return;
      }
      if (score == -1) {
        assert(am_i_winning);
        // Back to tie.
        return;
      }
      assert(false);
    }
  }

  bool ShouldIShare() const {
    const ll shared_entropy = my_number.SharedEntropy();
    const ll gathered_entropy = their_number.GatheredEntropy();
    if (shared_entropy == gathered_entropy) {
      // Doesn't matter, resolve to Algosia.
      return agent_type == AgentType::ALGOSIA;
    }
    if (shared_entropy < gathered_entropy) {
      // I shared less than I gathered, I need to share now.
      return true;
    }
    // I shared more than I gathered, I need to gather now.
    return false;
  }

  Move ReadTheirMove() {
    char c;
    cin >> c;
    return MoveFromChar(c);
  }

  int n;
  AgentType agent_type;
  const Preprocessing& preprocessing;
  SecretGenerator& secret_generator;

  MyNumber my_number;
  TheirNumber their_number;
};

AgentType ReadAgentType() {
  string who;
  cin >> who;
  if (who == "Algosia") {
    return AgentType::ALGOSIA;
  }
  if (who == "Bajtek") {
    return AgentType::BAJTEK;
  }
  assert(false);
}

int ReadInt() {
  int n;
  cin >> n;
  return n;
}

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);

  Preprocessing preprocessing;
  preprocessing.Run();

  const AgentType agent_type = ReadAgentType();

  const int n = ReadInt();
  const int t = ReadInt();

  SecretGenerator secret_generator(n, true);

  for (int i = 0; i < t; i++) {
    Agent agent(agent_type, n, preprocessing, secret_generator);
    agent.Run();
  }
  return 0;
}