#include "dzilib.h"
#include <bits/stdc++.h>
using std::vector;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
#define DEBUG(x) std::cerr << "Line " << __LINE__ << ": " << #x << " = " << x << "\n"
#define TRACE(x) std::cerr << "Line " << __LINE__ << ": " << #x "\n"

// Configuration.

constexpr bool randomize_offset = true;
constexpr u64 randomize_offset_limit = 10;
constexpr u64 rng_nonce = 0;
const u64 solve_primes[] = {2, 3};
// 200 MB
constexpr u64 divisor_limit = 50'000'000; // must be > 10^(17/3), 1e6+ OK

u64 choose_brute_limit(const u64 max_n, const u64 max_questions_per_test_case) {
  if (max_n <= 1'000'000'000 || max_questions_per_test_case >= 130) {
    return 500'000;
  } else if (max_questions_per_test_case >= 82) {
    return 2'000'000;
  } else if (max_questions_per_test_case >= 75) {
    return 4'000'000;
  } else {
    return 5'000'000;
  }
}

/// =================================

const std::uint32_t secret_key[8] = {
  235542195, 2150993683, 4252960442, 2004619671, 1424085794, 3389625356, 3726775613, 3633112236
};

namespace chacha_private {
  template <int shift>
  void rotate_left(std::uint32_t &x) {
    x = (x << shift) | (x >> (32 - shift));
  }

  inline void quarter_round(std::uint32_t &a, std::uint32_t &b, std::uint32_t &c, std::uint32_t &d) {
    a += b;
    d ^= a;
    rotate_left<16>(d);
    c += d;
    b ^= c;
    rotate_left<12>(b);
    a += b;
    d ^= a;
    rotate_left<8>(d);
    c += d;
    b ^= c;
    rotate_left<7>(b);
  }
}

template<int rounds>
void chacha(const std::uint32_t (&key)[8],
            const std::uint64_t nonce,
            const std::uint64_t counter,
            std::uint32_t (&output)[16])
{
  static_assert(rounds == 8 || rounds == 12 || rounds == 20);

  using namespace chacha_private;

  std::uint32_t input[16];
  std::memcpy(input + 0, "expand 32-byte k", 4 * sizeof(std::uint32_t));
  std::memcpy(input + 4, key, 8 * sizeof(std::uint32_t));
  std::memcpy(input + 12, &counter, 2 * sizeof(std::uint32_t));
  std::memcpy(input + 14, &nonce, 2 * sizeof(std::uint32_t));

  std::uint32_t x[16];
  std::memcpy(x, input, 16 * sizeof(std::uint32_t));

  for (int double_round = 0; double_round < rounds / 2; ++double_round) {
    quarter_round(x[0], x[4], x[8], x[12]);
    quarter_round(x[1], x[5], x[9], x[13]);
    quarter_round(x[2], x[6], x[10], x[14]);
    quarter_round(x[3], x[7], x[11], x[15]);

    quarter_round(x[0], x[5], x[10], x[15]);
    quarter_round(x[1], x[6], x[11], x[12]);
    quarter_round(x[2], x[7], x[8], x[13]);
    quarter_round(x[3], x[4], x[9], x[14]);
  }

  for (int i = 0; i < 16; ++i) {
    x[i] += input[i];
  }

  std::memcpy(output, x, 16 * sizeof(std::uint32_t));
}

class ChachaRandom {
public:
  using result_type = std::uint32_t;
  static constexpr result_type min() { return 0; }
  static constexpr result_type max() { return std::numeric_limits<result_type>::max(); }

  explicit ChachaRandom(const std::uint32_t (&key)[8], const std::uint64_t nonce);
  std::uint32_t operator()() {
    if (m_buffer_next == 16) {
      refill_buffer();
    }
    return m_buffer[m_buffer_next++];
  }

private:
  void refill_buffer();

  std::uint32_t m_chacha_key[8];
  std::uint64_t m_chacha_nonce = 0;
  std::uint64_t m_chacha_counter = 0;

  std::uint32_t m_buffer[16];
  int m_buffer_next = 16;
};

ChachaRandom::ChachaRandom(const std::uint32_t (&key)[8], const std::uint64_t nonce) {
  std::memcpy(m_chacha_key, key, 8 * sizeof(std::uint32_t));
  m_chacha_nonce = nonce;
}

void ChachaRandom::refill_buffer() {
  chacha<8>(m_chacha_key, m_chacha_nonce, m_chacha_counter++, m_buffer);
  m_buffer_next = 0;
}

// ====================================

struct FastDiv {
  u64 divisor;
  u64 shift;
  u64 m;

  FastDiv(u64 d) {
    divisor = d;
    u64 n = 1;
    while ((u64(1)<<n) < divisor) n += 1;

    m = (__uint128_t(1) << (64+n)) / divisor + 1;
    shift = n-1;
  }

  std::pair<u64, u64> divrem(u64 a) const {
    u64 t = (__uint128_t(m) * a) >> 64;
    u64 q = (t + ((a-t)>>1)) >> shift;
    u64 r = a - q * divisor;
    return {q, r};
  }
};

vector<u32> divisor_table;
vector<u32> primes;
vector<FastDiv> fast_divs;

void compute_primes() {
  divisor_table.assign(divisor_limit, 0);
  for (u64 p=2; p < divisor_limit; ++p) {
    if (divisor_table[p] != 0) continue;
    primes.push_back(p);
    fast_divs.push_back(FastDiv(p));
    divisor_table[p] = p;
    for (u64 x = p * p; x < divisor_limit; x += p) {
      if (divisor_table[x] == 0) {
        divisor_table[x] = p;
      }
    }
  }
}

u64 integer_sqrt(const u64 n) {
  u64 x = u64(std::sqrt(n));
  while (x * x > n) --x;
  while ((x+1) * (x+1) <= n) ++x;
  return x;
}

u64 integer_cube_root(const u64 n) {
  u64 x = u64(std::pow(n, 1.0/3));
  while (x * x * x > n) --x;
  while ((x+1) * (x+1) * (x+1) <= n) ++x;
  return x;
}

u64 mult_mod(const u64 a, const u64 b, const u64 m) {
  return __uint128_t(a) * __uint128_t(b) % m;
}

u64 power(u64 a, u64 b, u64 m) {
  u64 res = 1;
  while (b) {
    if (b&1u) res = mult_mod(res, a, m);
    b >>= 1;
    a = mult_mod(a, a, m);
  }
  return res;
}

bool miller_rabin(const u64 n, const u64 a) {
  u64 b = n-1;
  u64 s = 0;
  while (b%2 == 0) {
    b /= 2;
    ++s;
  }
  u64 x = power(a, b, n);
  for (u64 i=0; i<s; ++i) {
    const u64 y = mult_mod(x, x, n);
    if (y == 1 && x != 1 && x != n-1) {
      return false;
    }
    x = y;
  }
  if (x != 1) return false;
  return true;
}

bool large_prime_test(const u64 n) {
  for (const u64 p : primes) {
    if (p > 23) break;
    if (!miller_rabin(n, p)) return false;
  }
  return true;
}

bool is_prime(const u64 n) {
  if (n < divisor_limit) {
    return divisor_table[n] == n;
  } else {
    return large_prime_test(n);
  }
}

u64 compute_num_divisors(u64 n) {
  u64 result = 1;
  for (const u64 p : primes) {
    if (n < divisor_limit || p * p * p > n) break;
    if (n % p != 0) continue;
    u64 cnt = 1;
    n /= p;
    while (n % p == 0) {
      ++cnt;
      n /= p;
    }
    result *= (cnt + 1);
  }

  while (n > 1 && n < divisor_limit) {
    const u64 p = divisor_table[n];
    u64 cnt = 1;
    n /= p;
    while (n % p == 0) {
      ++cnt;
      n /= p;
    }
    result *= (cnt + 1);
  }

  if (n == 1) return result;
  const u64 a = integer_sqrt(n);
  if (a * a == n && is_prime(a)) {
    result *= 3;
  } else if (is_prime(n)) {
    result *= 2;
  } else {
    // n = p * q
    result *= 4;
  }
  return result;
}

// Returns 2 if may be false positive.
bool check_num_divisors(u64 n, u64 num_divisors) {
  if (n >= divisor_limit && num_divisors > 3) {
    u64 p_limit = integer_cube_root(n);
    for (u64 p_index = 0; p_index < primes.size(); ++p_index) {
      u64 p = primes[p_index];
      if (p > p_limit) break;
      const FastDiv &fast_div = fast_divs[p_index];
      auto [q, rem] = fast_div.divrem(n);
      if (rem != 0) continue;
      u64 cnt = 1;
      n = q;
      for (;;) {
        auto [q2, rem2] = fast_div.divrem(n);
        if (rem2 != 0) break;
        ++cnt;
        n = q2;
      }
      ++cnt;
      if (num_divisors % cnt != 0) return false;
      num_divisors /= cnt;
      if (n < divisor_limit || num_divisors <= 3) break;
      p_limit = integer_cube_root(n);
    }
  }

  while (n > 1 && n < divisor_limit) {
    const u64 p = divisor_table[n];
    u64 cnt = 1;
    n /= p;
    while (n % p == 0) {
      ++cnt;
      n /= p;
    }
    ++cnt;
    if (num_divisors % cnt != 0) return false;
    num_divisors /= cnt;
  }

  if (n == 1) return num_divisors == 1;
  if (num_divisors < 2 || num_divisors > 4) return false;
  const u64 a = integer_sqrt(n);
  if (a * a == n) {
    return num_divisors == 3;
  }
  if (num_divisors == 3) return false;
  
  return is_prime(n) == (num_divisors == 2);
}

u64 brute_compute_num_divisors(const u64 n) {
  u64 res = 0;
  u64 d = 1;
  for (; d*d < n; ++d) {
    if (n%d == 0) res += 2;
  }
  if (d*d==n) res += 1;
  return res;
}

bool is_power_of_2(const u32 n) {
  return n != 0 && (n & (n-1)) == 0;
}

ChachaRandom rng(secret_key, rng_nonce);

constexpr u64 none = -u64(1);

u64 max_offset;

// n = r (mod m)
struct Equation {
  u64 r;
  u64 m;
};

Equation trivial_equation() {
  return Equation{0, 1};
}

// n = r (mod p^k)
struct PowerEquation {
  u64 r;
  u64 p;
  u64 k;
};

Equation combine(Equation eq, const PowerEquation peq) {
  u64 pk = 1;
  for (u64 k = 1; k <= peq.k; ++k) {
    pk *= peq.p;
    while (eq.r % pk != peq.r % pk) {
      eq.r += eq.m;
    }
    eq.m *= peq.p;
  }
  return eq;
}

u64 find_offset_for(const Equation eq) {
  u64 offset = (eq.m - eq.r) % eq.m;
  assert(offset <= max_offset);
  if (randomize_offset) {
    u64 limit = std::min((max_offset - offset) / eq.m, randomize_offset_limit);
    std::uniform_int_distribution<u64> dist(0, limit);
    offset += eq.m * dist(rng);
  }
  return offset;
}

struct QuestionAnswer {
  u64 offset;
  u64 num_divisors;

  u64 difficulty() const {
    u64 odd_divisors = num_divisors;
    u64 pow2 = 0;
    while (odd_divisors % 2 == 0) { 
      odd_divisors /= 2;
      pow2++;
    }
    return -u64(1) - 100 * odd_divisors - pow2;
  }
};

QuestionAnswer ask_random_question() {
  std::uniform_int_distribution<u64> dist(0, max_offset);
  QuestionAnswer qa;
  qa.offset = dist(rng);
  qa.num_divisors = Ask(qa.offset);
  return qa;
}

bool matches(const QuestionAnswer qa, const u64 n) {
  return check_num_divisors(n + qa.offset, qa.num_divisors);
}

class PowerSolver {
public:
  explicit PowerSolver(const u64 p_): p(p_) {
    reset();
  }

  void reset() {
    options.clear();
    step = 1;
    p_step = p;
    if (is_power_of_2(k+step+1)) {
      step = 2;
      p_step = p * p;
    }

    for (u64 s = 0; s < p_step; ++s) {
      options.emplace(s, none);
    }
    refill_shots();
  }

  void refill_shots() {
    shots_remaining.clear();
    for (const auto [s, exception] : options) {
      for (u64 exc = 0; exc < p; ++exc) {
        if (exc == exception) continue;
        shots_remaining.emplace_back(s, exc);
      }
    }
    std::shuffle(shots_remaining.begin(), shots_remaining.end(), rng);
  }

  u64 known_range() const {
    return pk;
  }

  PowerEquation knowledge() const {
    return PowerEquation{r, p, k};
  }

  PowerEquation choose_question() {
    for (;;) {
      if (shots_remaining.empty()) {
        refill_shots();
      }

      const auto [s, exception] = shots_remaining.back();
      shots_remaining.pop_back();
      const auto it = options.find(s);
      if (it == options.end()) continue;
      // We wouldn't put it in the shots list.
      assert(it->second != exception);
      return PowerEquation{
        r + s * pk + exception * pk * p_step,
        p,
        k + step + 1
      };
    }
  }

  // Returns if significant progress.
  bool process_answer(const PowerEquation eq, const u64 num_divisors) {
    // If the remainder is valid mod p^(k+2), with one exception mod p^(k+3) we should have:
    // num_divisors is divisible by (k+3).
    // If this is not true, then we know an option is invalid.
    // If it is true, we learn nothing.
    if (num_divisors % (k + step + 1) == 0) {
      return false;
    }
    assert(eq.p == p && eq.k == k+step+1);
    const u64 s = eq.r / pk % p_step;
    const u64 exception = eq.r / (pk * p_step);

    const auto it = options.find(s);
    // We wouldn't ask a useless question.
    assert(it != options.end());
    if (it->second == none) {
      it->second = exception;
    } else {
      // We wouln't ask a useless question.
      assert(it->second != exception);
      options.erase(it);
      if (options.size() == 1) {
        upgrade();
        return true;
      }
    }
    return false;
  }

  void upgrade() {
    assert(options.size() == 1);
    const auto it = options.begin();
    const u64 s = it->first;
    r += s * pk;
    k += step;
    pk *= p_step;

    reset();
  }

private:
  // n = remainder (mod p^k)
  u64 p;
  u64 p_step; // p^step
  u64 step;
  u64 k = 0;
  u64 r = 0;
  u64 pk = 1; // p^k

  // maps s to exception, where:
  // s < p_step is such that n = r + s * p^k (mod p^(k+step))
  // exception < p is such that if s works, then:
  //   n = r + s * p^k + exception * p^(k+step) (mod p^(k+step+1))
  // exception can be none
  std::map<u64, u64> options;
  vector<std::pair<u64, u64>> shots_remaining;
};

class Solver {
public:
  explicit Solver(const u64 max_n1, const u64 brute_limit1) :
    max_n(max_n1),
    brute_limit(brute_limit1)
  {
    for (const u64 p : solve_primes) {
      solvers.emplace(p, PowerSolver(p));
    }
  }

  u64 solve() {
    phase_1();
    generate_n_options();
    phase_2();
    assert(n_options.size() == 1);
    return n_options[0];
  }

private:

  void phase_1() {
    for (;;) {
      if (phase_1_iteration()) {
        const u64 brute_size = max_n / known_range();
        if (brute_size <= brute_limit) {
          return;
        }
      }
    }
  }

  // Returns true if significant progress.
  bool phase_1_iteration() {
    const vector<PowerEquation> queries = generate_queries();

    Equation equation = trivial_equation();
    for (const PowerEquation &query : queries) {
      equation = combine(equation, query);
    }

    const u64 offset = find_offset_for(equation);
    const u64 num_divisors = Ask(offset);
    history.push_back(QuestionAnswer{offset, num_divisors});

    bool progress = false;
    for (const PowerEquation &query : queries) {
      const auto it = solvers.find(query.p);
      assert(it != solvers.end());
      PowerSolver &solver = it->second;
      if (solver.process_answer(query, num_divisors)) {
        progress = true;
      }
    }

    return progress;
  }

  u64 known_range() const {
    u64 range = 1;
    for (const auto &[p, solver] : solvers) {
      range *= solver.known_range();
    }
    return range;
  }

  vector<PowerEquation> generate_queries() {
    vector<PowerEquation> queries;

    for (auto &[p, solver] : solvers) {
      queries.push_back(solver.choose_question());
    }
    return queries;
  }

  Equation phase_1_solve() const {
    Equation total_knowledge = trivial_equation();
    for (const auto &[p, solver] : solvers) {
      const PowerEquation pe = solver.knowledge();
      total_knowledge = combine(total_knowledge, pe);
    }
    return total_knowledge;
  }

  void generate_n_options() {
    const Equation equation = phase_1_solve();
    u64 n = equation.r;
    if (n == 0) n += equation.m;
    for (;n <= max_n; n += equation.m) {
      n_options.push_back(n);
    }
  }

  void phase_2() {
    std::sort(history.begin(), history.end(),
        [](const QuestionAnswer a, const QuestionAnswer b) -> bool
        {
          return a.difficulty() < b.difficulty();
        }
    );

    for (const QuestionAnswer qa : history) {
      if (n_options.size() <= 1) return;
      filter_options(qa);
    }
    // Very unlikely this will happen.
    while (n_options.size() > 1) {
      const QuestionAnswer qa = ask_random_question();
      filter_options(qa);
    }
  }

  void filter_options(const QuestionAnswer qa) {
    auto it = std::remove_if(n_options.begin(), n_options.end(),
        [qa](const u64 n) -> bool {
          return !matches(qa, n);
        }
    );
    n_options.erase(it, n_options.end());
  }

  u64 max_n;
  u64 brute_limit;
  std::map<u64, PowerSolver> solvers;
  vector<QuestionAnswer> history;
  vector<u64> n_options;
};

void test_fast_div() {
  std::uniform_int_distribution<u64> dist{1, 1000000000000};
  std::uniform_int_distribution<u64> dist2{1, 1000000000000000};
  for (u64 i=0;i<1000;++i) {
    u64 d = dist(rng);
    FastDiv fd(d);
    u64 n = dist2(rng);
    assert((fd.divrem(n) == std::pair<u64, u64>{n/d, n%d}));
  }
}

void test_num_divisors() {
  for (u64 n=1; n<=1000000; ++n) {
    assert(brute_compute_num_divisors(n) == compute_num_divisors(n));
  }
  assert(compute_num_divisors(u64(100000007) * 100000007) == 3);
  assert(compute_num_divisors(u64(100000007) * 100000037) == 4);
  assert(compute_num_divisors(100000000000031) == 2);
}


int main() {
  compute_primes();

  const u64 ntc = GetT();
  const u64 max_n = GetN();
  const u64 max_questions = GetQ();
  max_offset = GetC();
  const u64 brute_limit = choose_brute_limit(max_n, max_questions / ntc);

  for (u64 tc = 0; tc < ntc; ++tc) {
    Solver solver(max_n, brute_limit);
    const u64 n = solver.solve();
    Answer(n);
  }
}

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#include "dzilib.h"
#include <bits/stdc++.h>
using std::vector;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
#define DEBUG(x) std::cerr << "Line " << __LINE__ << ": " << #x << " = " << x << "\n"
#define TRACE(x) std::cerr << "Line " << __LINE__ << ": " << #x "\n"

// Configuration.

constexpr bool randomize_offset = true;
constexpr u64 randomize_offset_limit = 10;
constexpr u64 rng_nonce = 0;
const u64 solve_primes[] = {2, 3};
// 200 MB
constexpr u64 divisor_limit = 50'000'000; // must be > 10^(17/3), 1e6+ OK

u64 choose_brute_limit(const u64 max_n, const u64 max_questions_per_test_case) {
  if (max_n <= 1'000'000'000 || max_questions_per_test_case >= 130) {
    return 500'000;
  } else if (max_questions_per_test_case >= 82) {
    return 2'000'000;
  } else if (max_questions_per_test_case >= 75) {
    return 4'000'000;
  } else {
    return 5'000'000;
  }
}

/// =================================

const std::uint32_t secret_key[8] = {
  235542195, 2150993683, 4252960442, 2004619671, 1424085794, 3389625356, 3726775613, 3633112236
};

namespace chacha_private {
  template <int shift>
  void rotate_left(std::uint32_t &x) {
    x = (x << shift) | (x >> (32 - shift));
  }

  inline void quarter_round(std::uint32_t &a, std::uint32_t &b, std::uint32_t &c, std::uint32_t &d) {
    a += b;
    d ^= a;
    rotate_left<16>(d);
    c += d;
    b ^= c;
    rotate_left<12>(b);
    a += b;
    d ^= a;
    rotate_left<8>(d);
    c += d;
    b ^= c;
    rotate_left<7>(b);
  }
}

template<int rounds>
void chacha(const std::uint32_t (&key)[8],
            const std::uint64_t nonce,
            const std::uint64_t counter,
            std::uint32_t (&output)[16])
{
  static_assert(rounds == 8 || rounds == 12 || rounds == 20);

  using namespace chacha_private;

  std::uint32_t input[16];
  std::memcpy(input + 0, "expand 32-byte k", 4 * sizeof(std::uint32_t));
  std::memcpy(input + 4, key, 8 * sizeof(std::uint32_t));
  std::memcpy(input + 12, &counter, 2 * sizeof(std::uint32_t));
  std::memcpy(input + 14, &nonce, 2 * sizeof(std::uint32_t));

  std::uint32_t x[16];
  std::memcpy(x, input, 16 * sizeof(std::uint32_t));

  for (int double_round = 0; double_round < rounds / 2; ++double_round) {
    quarter_round(x[0], x[4], x[8], x[12]);
    quarter_round(x[1], x[5], x[9], x[13]);
    quarter_round(x[2], x[6], x[10], x[14]);
    quarter_round(x[3], x[7], x[11], x[15]);

    quarter_round(x[0], x[5], x[10], x[15]);
    quarter_round(x[1], x[6], x[11], x[12]);
    quarter_round(x[2], x[7], x[8], x[13]);
    quarter_round(x[3], x[4], x[9], x[14]);
  }

  for (int i = 0; i < 16; ++i) {
    x[i] += input[i];
  }

  std::memcpy(output, x, 16 * sizeof(std::uint32_t));
}

class ChachaRandom {
public:
  using result_type = std::uint32_t;
  static constexpr result_type min() { return 0; }
  static constexpr result_type max() { return std::numeric_limits<result_type>::max(); }

  explicit ChachaRandom(const std::uint32_t (&key)[8], const std::uint64_t nonce);
  std::uint32_t operator()() {
    if (m_buffer_next == 16) {
      refill_buffer();
    }
    return m_buffer[m_buffer_next++];
  }

private:
  void refill_buffer();

  std::uint32_t m_chacha_key[8];
  std::uint64_t m_chacha_nonce = 0;
  std::uint64_t m_chacha_counter = 0;

  std::uint32_t m_buffer[16];
  int m_buffer_next = 16;
};

ChachaRandom::ChachaRandom(const std::uint32_t (&key)[8], const std::uint64_t nonce) {
  std::memcpy(m_chacha_key, key, 8 * sizeof(std::uint32_t));
  m_chacha_nonce = nonce;
}

void ChachaRandom::refill_buffer() {
  chacha<8>(m_chacha_key, m_chacha_nonce, m_chacha_counter++, m_buffer);
  m_buffer_next = 0;
}

// ====================================

struct FastDiv {
  u64 divisor;
  u64 shift;
  u64 m;

  FastDiv(u64 d) {
    divisor = d;
    u64 n = 1;
    while ((u64(1)<<n) < divisor) n += 1;

    m = (__uint128_t(1) << (64+n)) / divisor + 1;
    shift = n-1;
  }

  std::pair<u64, u64> divrem(u64 a) const {
    u64 t = (__uint128_t(m) * a) >> 64;
    u64 q = (t + ((a-t)>>1)) >> shift;
    u64 r = a - q * divisor;
    return {q, r};
  }
};

vector<u32> divisor_table;
vector<u32> primes;
vector<FastDiv> fast_divs;

void compute_primes() {
  divisor_table.assign(divisor_limit, 0);
  for (u64 p=2; p < divisor_limit; ++p) {
    if (divisor_table[p] != 0) continue;
    primes.push_back(p);
    fast_divs.push_back(FastDiv(p));
    divisor_table[p] = p;
    for (u64 x = p * p; x < divisor_limit; x += p) {
      if (divisor_table[x] == 0) {
        divisor_table[x] = p;
      }
    }
  }
}

u64 integer_sqrt(const u64 n) {
  u64 x = u64(std::sqrt(n));
  while (x * x > n) --x;
  while ((x+1) * (x+1) <= n) ++x;
  return x;
}

u64 integer_cube_root(const u64 n) {
  u64 x = u64(std::pow(n, 1.0/3));
  while (x * x * x > n) --x;
  while ((x+1) * (x+1) * (x+1) <= n) ++x;
  return x;
}

u64 mult_mod(const u64 a, const u64 b, const u64 m) {
  return __uint128_t(a) * __uint128_t(b) % m;
}

u64 power(u64 a, u64 b, u64 m) {
  u64 res = 1;
  while (b) {
    if (b&1u) res = mult_mod(res, a, m);
    b >>= 1;
    a = mult_mod(a, a, m);
  }
  return res;
}

bool miller_rabin(const u64 n, const u64 a) {
  u64 b = n-1;
  u64 s = 0;
  while (b%2 == 0) {
    b /= 2;
    ++s;
  }
  u64 x = power(a, b, n);
  for (u64 i=0; i<s; ++i) {
    const u64 y = mult_mod(x, x, n);
    if (y == 1 && x != 1 && x != n-1) {
      return false;
    }
    x = y;
  }
  if (x != 1) return false;
  return true;
}

bool large_prime_test(const u64 n) {
  for (const u64 p : primes) {
    if (p > 23) break;
    if (!miller_rabin(n, p)) return false;
  }
  return true;
}

bool is_prime(const u64 n) {
  if (n < divisor_limit) {
    return divisor_table[n] == n;
  } else {
    return large_prime_test(n);
  }
}

u64 compute_num_divisors(u64 n) {
  u64 result = 1;
  for (const u64 p : primes) {
    if (n < divisor_limit || p * p * p > n) break;
    if (n % p != 0) continue;
    u64 cnt = 1;
    n /= p;
    while (n % p == 0) {
      ++cnt;
      n /= p;
    }
    result *= (cnt + 1);
  }

  while (n > 1 && n < divisor_limit) {
    const u64 p = divisor_table[n];
    u64 cnt = 1;
    n /= p;
    while (n % p == 0) {
      ++cnt;
      n /= p;
    }
    result *= (cnt + 1);
  }

  if (n == 1) return result;
  const u64 a = integer_sqrt(n);
  if (a * a == n && is_prime(a)) {
    result *= 3;
  } else if (is_prime(n)) {
    result *= 2;
  } else {
    // n = p * q
    result *= 4;
  }
  return result;
}

// Returns 2 if may be false positive.
bool check_num_divisors(u64 n, u64 num_divisors) {
  if (n >= divisor_limit && num_divisors > 3) {
    u64 p_limit = integer_cube_root(n);
    for (u64 p_index = 0; p_index < primes.size(); ++p_index) {
      u64 p = primes[p_index];
      if (p > p_limit) break;
      const FastDiv &fast_div = fast_divs[p_index];
      auto [q, rem] = fast_div.divrem(n);
      if (rem != 0) continue;
      u64 cnt = 1;
      n = q;
      for (;;) {
        auto [q2, rem2] = fast_div.divrem(n);
        if (rem2 != 0) break;
        ++cnt;
        n = q2;
      }
      ++cnt;
      if (num_divisors % cnt != 0) return false;
      num_divisors /= cnt;
      if (n < divisor_limit || num_divisors <= 3) break;
      p_limit = integer_cube_root(n);
    }
  }

  while (n > 1 && n < divisor_limit) {
    const u64 p = divisor_table[n];
    u64 cnt = 1;
    n /= p;
    while (n % p == 0) {
      ++cnt;
      n /= p;
    }
    ++cnt;
    if (num_divisors % cnt != 0) return false;
    num_divisors /= cnt;
  }

  if (n == 1) return num_divisors == 1;
  if (num_divisors < 2 || num_divisors > 4) return false;
  const u64 a = integer_sqrt(n);
  if (a * a == n) {
    return num_divisors == 3;
  }
  if (num_divisors == 3) return false;
  
  return is_prime(n) == (num_divisors == 2);
}

u64 brute_compute_num_divisors(const u64 n) {
  u64 res = 0;
  u64 d = 1;
  for (; d*d < n; ++d) {
    if (n%d == 0) res += 2;
  }
  if (d*d==n) res += 1;
  return res;
}

bool is_power_of_2(const u32 n) {
  return n != 0 && (n & (n-1)) == 0;
}

ChachaRandom rng(secret_key, rng_nonce);

constexpr u64 none = -u64(1);

u64 max_offset;

// n = r (mod m)
struct Equation {
  u64 r;
  u64 m;
};

Equation trivial_equation() {
  return Equation{0, 1};
}

// n = r (mod p^k)
struct PowerEquation {
  u64 r;
  u64 p;
  u64 k;
};

Equation combine(Equation eq, const PowerEquation peq) {
  u64 pk = 1;
  for (u64 k = 1; k <= peq.k; ++k) {
    pk *= peq.p;
    while (eq.r % pk != peq.r % pk) {
      eq.r += eq.m;
    }
    eq.m *= peq.p;
  }
  return eq;
}

u64 find_offset_for(const Equation eq) {
  u64 offset = (eq.m - eq.r) % eq.m;
  assert(offset <= max_offset);
  if (randomize_offset) {
    u64 limit = std::min((max_offset - offset) / eq.m, randomize_offset_limit);
    std::uniform_int_distribution<u64> dist(0, limit);
    offset += eq.m * dist(rng);
  }
  return offset;
}

struct QuestionAnswer {
  u64 offset;
  u64 num_divisors;

  u64 difficulty() const {
    u64 odd_divisors = num_divisors;
    u64 pow2 = 0;
    while (odd_divisors % 2 == 0) { 
      odd_divisors /= 2;
      pow2++;
    }
    return -u64(1) - 100 * odd_divisors - pow2;
  }
};

QuestionAnswer ask_random_question() {
  std::uniform_int_distribution<u64> dist(0, max_offset);
  QuestionAnswer qa;
  qa.offset = dist(rng);
  qa.num_divisors = Ask(qa.offset);
  return qa;
}

bool matches(const QuestionAnswer qa, const u64 n) {
  return check_num_divisors(n + qa.offset, qa.num_divisors);
}

class PowerSolver {
public:
  explicit PowerSolver(const u64 p_): p(p_) {
    reset();
  }

  void reset() {
    options.clear();
    step = 1;
    p_step = p;
    if (is_power_of_2(k+step+1)) {
      step = 2;
      p_step = p * p;
    }

    for (u64 s = 0; s < p_step; ++s) {
      options.emplace(s, none);
    }
    refill_shots();
  }

  void refill_shots() {
    shots_remaining.clear();
    for (const auto [s, exception] : options) {
      for (u64 exc = 0; exc < p; ++exc) {
        if (exc == exception) continue;
        shots_remaining.emplace_back(s, exc);
      }
    }
    std::shuffle(shots_remaining.begin(), shots_remaining.end(), rng);
  }

  u64 known_range() const {
    return pk;
  }

  PowerEquation knowledge() const {
    return PowerEquation{r, p, k};
  }

  PowerEquation choose_question() {
    for (;;) {
      if (shots_remaining.empty()) {
        refill_shots();
      }

      const auto [s, exception] = shots_remaining.back();
      shots_remaining.pop_back();
      const auto it = options.find(s);
      if (it == options.end()) continue;
      // We wouldn't put it in the shots list.
      assert(it->second != exception);
      return PowerEquation{
        r + s * pk + exception * pk * p_step,
        p,
        k + step + 1
      };
    }
  }

  // Returns if significant progress.
  bool process_answer(const PowerEquation eq, const u64 num_divisors) {
    // If the remainder is valid mod p^(k+2), with one exception mod p^(k+3) we should have:
    // num_divisors is divisible by (k+3).
    // If this is not true, then we know an option is invalid.
    // If it is true, we learn nothing.
    if (num_divisors % (k + step + 1) == 0) {
      return false;
    }
    assert(eq.p == p && eq.k == k+step+1);
    const u64 s = eq.r / pk % p_step;
    const u64 exception = eq.r / (pk * p_step);

    const auto it = options.find(s);
    // We wouldn't ask a useless question.
    assert(it != options.end());
    if (it->second == none) {
      it->second = exception;
    } else {
      // We wouln't ask a useless question.
      assert(it->second != exception);
      options.erase(it);
      if (options.size() == 1) {
        upgrade();
        return true;
      }
    }
    return false;
  }

  void upgrade() {
    assert(options.size() == 1);
    const auto it = options.begin();
    const u64 s = it->first;
    r += s * pk;
    k += step;
    pk *= p_step;

    reset();
  }

private:
  // n = remainder (mod p^k)
  u64 p;
  u64 p_step; // p^step
  u64 step;
  u64 k = 0;
  u64 r = 0;
  u64 pk = 1; // p^k

  // maps s to exception, where:
  // s < p_step is such that n = r + s * p^k (mod p^(k+step))
  // exception < p is such that if s works, then:
  //   n = r + s * p^k + exception * p^(k+step) (mod p^(k+step+1))
  // exception can be none
  std::map<u64, u64> options;
  vector<std::pair<u64, u64>> shots_remaining;
};

class Solver {
public:
  explicit Solver(const u64 max_n1, const u64 brute_limit1) :
    max_n(max_n1),
    brute_limit(brute_limit1)
  {
    for (const u64 p : solve_primes) {
      solvers.emplace(p, PowerSolver(p));
    }
  }

  u64 solve() {
    phase_1();
    generate_n_options();
    phase_2();
    assert(n_options.size() == 1);
    return n_options[0];
  }

private:

  void phase_1() {
    for (;;) {
      if (phase_1_iteration()) {
        const u64 brute_size = max_n / known_range();
        if (brute_size <= brute_limit) {
          return;
        }
      }
    }
  }

  // Returns true if significant progress.
  bool phase_1_iteration() {
    const vector<PowerEquation> queries = generate_queries();

    Equation equation = trivial_equation();
    for (const PowerEquation &query : queries) {
      equation = combine(equation, query);
    }

    const u64 offset = find_offset_for(equation);
    const u64 num_divisors = Ask(offset);
    history.push_back(QuestionAnswer{offset, num_divisors});

    bool progress = false;
    for (const PowerEquation &query : queries) {
      const auto it = solvers.find(query.p);
      assert(it != solvers.end());
      PowerSolver &solver = it->second;
      if (solver.process_answer(query, num_divisors)) {
        progress = true;
      }
    }

    return progress;
  }

  u64 known_range() const {
    u64 range = 1;
    for (const auto &[p, solver] : solvers) {
      range *= solver.known_range();
    }
    return range;
  }

  vector<PowerEquation> generate_queries() {
    vector<PowerEquation> queries;

    for (auto &[p, solver] : solvers) {
      queries.push_back(solver.choose_question());
    }
    return queries;
  }

  Equation phase_1_solve() const {
    Equation total_knowledge = trivial_equation();
    for (const auto &[p, solver] : solvers) {
      const PowerEquation pe = solver.knowledge();
      total_knowledge = combine(total_knowledge, pe);
    }
    return total_knowledge;
  }

  void generate_n_options() {
    const Equation equation = phase_1_solve();
    u64 n = equation.r;
    if (n == 0) n += equation.m;
    for (;n <= max_n; n += equation.m) {
      n_options.push_back(n);
    }
  }

  void phase_2() {
    std::sort(history.begin(), history.end(),
        [](const QuestionAnswer a, const QuestionAnswer b) -> bool
        {
          return a.difficulty() < b.difficulty();
        }
    );

    for (const QuestionAnswer qa : history) {
      if (n_options.size() <= 1) return;
      filter_options(qa);
    }
    // Very unlikely this will happen.
    while (n_options.size() > 1) {
      const QuestionAnswer qa = ask_random_question();
      filter_options(qa);
    }
  }

  void filter_options(const QuestionAnswer qa) {
    auto it = std::remove_if(n_options.begin(), n_options.end(),
        [qa](const u64 n) -> bool {
          return !matches(qa, n);
        }
    );
    n_options.erase(it, n_options.end());
  }

  u64 max_n;
  u64 brute_limit;
  std::map<u64, PowerSolver> solvers;
  vector<QuestionAnswer> history;
  vector<u64> n_options;
};

void test_fast_div() {
  std::uniform_int_distribution<u64> dist{1, 1000000000000};
  std::uniform_int_distribution<u64> dist2{1, 1000000000000000};
  for (u64 i=0;i<1000;++i) {
    u64 d = dist(rng);
    FastDiv fd(d);
    u64 n = dist2(rng);
    assert((fd.divrem(n) == std::pair<u64, u64>{n/d, n%d}));
  }
}

void test_num_divisors() {
  for (u64 n=1; n<=1000000; ++n) {
    assert(brute_compute_num_divisors(n) == compute_num_divisors(n));
  }
  assert(compute_num_divisors(u64(100000007) * 100000007) == 3);
  assert(compute_num_divisors(u64(100000007) * 100000037) == 4);
  assert(compute_num_divisors(100000000000031) == 2);
}


int main() {
  compute_primes();

  const u64 ntc = GetT();
  const u64 max_n = GetN();
  const u64 max_questions = GetQ();
  max_offset = GetC();
  const u64 brute_limit = choose_brute_limit(max_n, max_questions / ntc);

  for (u64 tc = 0; tc < ntc; ++tc) {
    Solver solver(max_n, brute_limit);
    const u64 n = solver.solve();
    Answer(n);
  }
}