#include "dzilib.h"
#include<bits/stdc++.h>
using namespace std;
using LL=long long;
#define FOR(i,l,r)for(int i=(l);i<=(r);++i)
#define REP(i,n)FOR(i,0,(n)-1)
#define ssize(x)int(x.size())
#ifdef DEBUG
auto operator<<(auto&o,auto x)->decltype(x.end(),o);
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<", "<<get<3>(t)<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

namespace yosupo {
	uint64_t gcd_stein_impl( uint64_t x, uint64_t y ) {
    if( x == y ) { return x; }
    const uint64_t a = y - x;
    const uint64_t b = x - y;
    const int n = __builtin_ctzll( b );
    const uint64_t s = x < y ? a : b;
    const uint64_t t = x < y ? x : y;
    return gcd_stein_impl( s >> n, t );
}

uint64_t gcd_stein( uint64_t x, uint64_t y ) {
    if( x == 0 ) { return y; }
    if( y == 0 ) { return x; }
    const int n = __builtin_ctzll( x );
    const int m = __builtin_ctzll( y );
    return gcd_stein_impl( x >> n, y >> m ) << ( n < m ? n : m );
}

// ---- is_prime ----

uint64_t mod_pow( uint64_t x, uint64_t y, uint64_t mod ) {
    uint64_t ret = 1;
    uint64_t acc = x;
    for( ; y; y >>= 1 ) {
        if( y & 1 ) {
            ret = __uint128_t(ret) * acc % mod;
        }
        acc = __uint128_t(acc) * acc % mod;
    }
    return ret;
}

bool miller_rabin( uint64_t n, const std::initializer_list<uint64_t>& as ) {
    return std::all_of( as.begin(), as.end(), [n]( uint64_t a ) {
        if( n <= a ) { return true; }

        int e = __builtin_ctzll( n - 1 );
        uint64_t z = mod_pow( a, ( n - 1 ) >> e, n );
        if( z == 1 || z == n - 1 ) { return true; }

        while( --e ) {
            z = __uint128_t(z) * z % n;
            if( z == 1 ) { return false; }
            if( z == n - 1 ) { return true; }
        }

        return false;
    });
}

bool is_prime( uint64_t n ) {
    if( n == 2 ) { return true; }
    if( n % 2 == 0 ) { return false; }
    if( n < 4759123141 ) { return miller_rabin( n, { 2, 7, 61 } ); }
    return miller_rabin( n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 } );
}

// ---- Montgomery ----

class Montgomery {
    uint64_t mod;
    uint64_t R;
public:
    Montgomery( uint64_t n ) : mod(n), R(n) {
       for( size_t i = 0; i < 5; ++i ) {
          R *= 2 - mod * R;
       }
    }

    uint64_t fma( uint64_t a, uint64_t b, uint64_t c ) const {
        const __uint128_t d = __uint128_t(a) * b;
        const uint64_t    e = c + mod + ( d >> 64 );
        const uint64_t    f = uint64_t(d) * R;
        const uint64_t    g = ( __uint128_t(f) * mod ) >> 64;
        return e - g;
    }

    uint64_t mul( uint64_t a, uint64_t b ) const {
        return fma( a, b, 0 );
    }
};

// ---- Pollard's rho algorithm ----

uint64_t pollard_rho( uint64_t n ) {
    if( n % 2 == 0 ) { return 2; }
    const Montgomery m( n );

    constexpr uint64_t C1 = 1;
    constexpr uint64_t C2 = 2;
    constexpr uint64_t M = 512;

    uint64_t Z1 = 1;
    uint64_t Z2 = 2;
retry:
    uint64_t z1 = Z1;
    uint64_t z2 = Z2;
    for( size_t k = M; ; k *= 2 ) {
        const uint64_t x1 = z1 + n;
        const uint64_t x2 = z2 + n;
        for( size_t j = 0; j < k; j += M ) {
            const uint64_t y1 = z1;
            const uint64_t y2 = z2;

            uint64_t q1 = 1;
            uint64_t q2 = 2;
            z1 = m.fma( z1, z1, C1 );
            z2 = m.fma( z2, z2, C2 );
            for( size_t i = 0; i < M; ++i ) {
                const uint64_t t1 = x1 - z1;
                const uint64_t t2 = x2 - z2;
                z1 = m.fma( z1, z1, C1 );
                z2 = m.fma( z2, z2, C2 );
                q1 = m.mul( q1, t1 );
                q2 = m.mul( q2, t2 );
            }
            q1 = m.mul( q1, x1 - z1 );
            q2 = m.mul( q2, x2 - z2 );

            const uint64_t q3 = m.mul( q1, q2 );
            const uint64_t g3 = gcd_stein( n, q3 );
            if( g3 == 1 ) { continue; }
            if( g3 != n ) { return g3; }

            const uint64_t g1 = gcd_stein( n, q1 );
            const uint64_t g2 = gcd_stein( n, q2 );

            const uint64_t C = g1 != 1 ? C1 : C2;
            const uint64_t x = g1 != 1 ? x1 : x2;
            uint64_t       z = g1 != 1 ? y1 : y2;
            uint64_t       g = g1 != 1 ? g1 : g2;

            if( g == n ) {
                do {
                    z = m.fma( z, z, C );
                    g = gcd_stein( n, x - z );
                } while( g == 1 );
            }
            if( g != n ) {
                return g;
            }

            Z1 += 2;
            Z2 += 2;
            goto retry;
        }
    }
}

void factorize_impl( uint64_t n, std::vector<uint64_t>& ret ) {
    if( n <= 1 ) { return; }
    if( is_prime( n ) ) { ret.push_back( n ); return; }

    const uint64_t p = pollard_rho( n );

    factorize_impl( p, ret );
    factorize_impl( n / p, ret );
}

std::vector<uint64_t> factorize( uint64_t n ) {
    std::vector<uint64_t> ret;
    factorize_impl( n, ret );
    std::sort( ret.begin(), ret.end() );
    return ret;
}

}


tuple<LL, LL, LL> extended_gcd(LL a, LL b) {
	if(a == 0)
		return {b, 0, 1};
	auto [gcd, x, y] = extended_gcd(b % a, a);
	return {gcd, y - x * (b / a), x};
}
LL crt(LL a, LL m, LL b, LL n) {
	if(n > m) swap(a, b), swap(m, n);
	auto [d, x, y] = extended_gcd(m, n);
	assert((a - b) % d == 0);
	LL ret = (b - a) % n * x % n / d * m + a;
	return ret < 0 ? ret + m * n / d : ret;
}

mt19937_64 rng_64(0);
LL rd(LL l, LL r) {
	return uniform_int_distribution<LL>(l, r)(rng_64);
}

namespace acmlib {

vector<bool> comp;
vector<int> primes;
void sieve(int n) {
	primes.clear();
	comp.resize(n + 1);
	FOR(i, 2, n) {
		if (!comp[i]) primes.emplace_back(i);
		for (int p : primes) {
			int x = i * p;
			if (x > n) break;
			comp[x] = true;
			if (i % p == 0) break;
		}
	}
}

} // acmlib

struct Sieve {
	LL l, r;
	vector<LL> val, cnt;
	Sieve(LL n) : l(-1), r(-1) {
		const int s = int(sqrt(n) + 10);
		acmlib::sieve(s);
	}
	void sieve(LL _l, LL _r) {
		l = max(1ll, _l);
		r = _r;
		assert(l <= r);
		const int len = int(r - l + 1);
		val.resize(len);
		iota(val.begin(), val.end(), l);
		cnt.resize(len);
		fill(cnt.begin(), cnt.end(), 1);
		for (int p : acmlib::primes) {
			for (LL n = (l + p - 1) / p * p; n <= r; n += p) {
				int cur = 1;
				while (val[n - l] % p == 0) {
					++cur;
					val[n - l] /= p;
				}
				cnt[n - l] *= cur;
			}
		}
		REP(i, len) {
			if (val[i] > 1)
				cnt[i] *= 2;
		}
	}
	LL operator()(LL n) {
		assert(n >= l and n <= r);
		return cnt[n - l];
	}
};

LL llmul(LL a, LL b, LL m) {
	return LL(__int128_t(a) * b % m);
}
LL llpowi(LL a, LL n, LL m) {
	for (LL ret = 1;; n /= 2) {
		if (n == 0)
			return ret;
		if (n % 2)
			ret = llmul(ret, a, m);
		a = llmul(a, a, m);
	}
}
bool miller_rabin(LL n) {
	if(n < 2) return false;
	int r = 0;
	LL d = n - 1;
	while(d % 2 == 0)
		d /= 2, r++;
	for(int a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
		if (a % n == 0) continue;
		LL x = llpowi(a, d, n);
		if(x == 1 || x == n - 1)
			continue;
		bool composite = true;
		REP(i, r - 1) {
			x = llmul(x, x, n);
			if(x == n - 1) {
				composite = false;
				break;
			}
		}
		if(composite) return false;
	}
	return true;
}
// BEGIN HASH
LL rho_pollard(LL n) {
	if(n % 2 == 0) return 2;
	for(LL i = 1;; i++) {
		auto f = [&](LL x) { return (llmul(x, x, n) + i) % n; };
		LL x = 2, y = f(x), p;
		while((p = __gcd(n - x + y, n)) == 1)
			x = f(x), y = f(f(y));
		if(p != n) return p;
	}
}
vector<LL> factor(LL n) {
	if(n == 1) return {};
	if(miller_rabin(n)) return {n};
	LL x = rho_pollard(n);
	auto l = factor(x), r = factor(n / x);
	l.insert(l.end(), r.begin(), r.end());
	return l;
} // END HASH
vector<pair<LL, int>> get_pairs(LL n) {
	/*
	auto v = factor(n);
	sort(v.begin(), v.end());
	*/
	auto v = yosupo::factorize(n);
	vector<pair<LL, int>> ret;
	REP(i, ssize(v)) {
		int x = i + 1;
		while (x < ssize(v) and v[x] == v[i])
			++x;
		ret.emplace_back(v[i], x - i);
		i = x - 1;
	}
	return ret;
}
int cnt_factors(LL n) {
	int ret = 1;
	for (auto [_, x] : get_pairs(n))
		ret *= x + 1;
	return ret;
}
vector<LL> all_factors(LL n) {
	auto v = get_pairs(n);
	vector<LL> ret;
	function<void(LL,int)> gen = [&](LL val, int p) {
		if (p == ssize(v)) {
			ret.emplace_back(val);
			return;
		}
		auto [x, cnt] = v[p];
		gen(val, p + 1);
		REP(i, cnt) {
			val *= x;
			gen(val, p + 1);
		}
	};
	gen(1, 0);
	return ret;
}

int main() {
	cin.tie(0)->sync_with_stdio(0);

	const int t = GetT();
	const int q = GetQ();
	const int limit = q / t;
	const LL n = GetN();
	debug(t, q, limit, n);

	Sieve s(10 * n);

	const int sub2 = int(1e6);
	const int sub3 = int(1e9);

	if (n <= sub2) {
		s.sieve(1, 3 * n);
		REP(tt, t) {
			vector<pair<LL, LL>> queries(limit);
			for (auto& [y, ans] : queries) {
				y = rd(0, n);
				ans = Ask(y);
			}
			auto ok = [&](int x) {
				for (auto [y, ans] : queries) {
					if (s(x + y) != ans) {
						return false;
					}
				}
				return true;
			};
			bool found = false;
			FOR(x, 1, n) {
				if (ok(x)) {
					Answer(x);
					found = true;
					break;
				}
			}
			assert(found);
		}
		return 0;
	}

	if (n == sub3) {
		const int query_range = n;
		const int L = n + query_range;
		acmlib::sieve(1e6);
		const auto primes = acmlib::primes;
		REP(tt, t) {
			vector<pair<LL, LL>> queries(limit);
			for (auto& [y, ans] : queries) {
				y = rd(0, query_range);
				ans = Ask(y);
			}
			auto ok = [&](LL x) {
				if (x < 1 or x > n)
					return false;
				for (auto [y, ans] : queries) {
					if (cnt_factors(x + y) != ans) {
						return false;
					}
				}
				return true;
			};

			pair<LL, LL> best;
			for (auto [y, ans] : queries)
				best = max(best, pair(ans, y));
			const auto [val, y] = best;
			debug(val, y);

			bool found = false;
			vector<int> exponents;
			function<void(LL)> rec = [&](LL left) {
				if (left == 1) {
					function<void(LL, int, int)> gen = [&](LL x, int id_expo, int id_prime) {
						if (id_expo == ssize(exponents)) {
							if (ok(x - y)) {
								debug(x - y);
								Answer(x - y);
								found = true;
							}
							return;
						}
						LL lower_bound = x;
						FOR(i, id_expo, ssize(exponents) - 1) {
							REP(j, exponents[i]) {
								lower_bound *= primes[id_prime + i - id_expo];
								if (lower_bound > L)
									return;
							}
						}
						FOR(i, id_prime, ssize(primes)) {
							LL cur = x;
							REP(j, exponents[id_expo]) {
								cur *= primes[i];
								if (cur > L)
									return;
							}
							gen(cur, id_expo + 1, i + 1);
							if (found)
								return;
						}
					};
					gen(1, 0, 0);
					return;
				}
				for (auto f : all_factors(left)) {
					if (f == 1)
						continue;
					exponents.emplace_back(f - 1);
					rec(left / f);
					exponents.pop_back();
				}
			};
			rec(val);
			assert(found);
		}
		return 0;
	}

	acmlib::sieve(100);
	const auto primes = acmlib::primes;
	const vector<int> squares = {4, 9};
	const int S = ssize(primes);
	const int Q = ssize(squares);

	REP(tt, t) {
		const LL q_min = 1e8;
		const LL q_max = 1e9;

		vector<pair<LL, LL>> queries(limit);
		int hura = 0;
		vector<int> prime_queries;
		vector<int> nearly_primes;
		vector<int> nearly_primes2, can6, can12;
		map<int, int> hh;
		for (auto& [y, ans] : queries) {
			y = rd(q_min, q_max);
			ans = Ask(y);
			if (ans == 2) {
				prime_queries.emplace_back(y);
			}
			if (ans == 4) {
				nearly_primes.emplace_back(y);
			}
			if (ans == 8) {
				nearly_primes2.emplace_back(y);
			}
			if (ans == 6) {
				can6.emplace_back(y);
			}
			if (ans == 12) {
				can12.emplace_back(y);
			}
			hh[ans]++;
		}
		vector<pair<int, int>> yy(hh.begin(), hh.end());
		for (auto& [a, b] : yy)
			swap(a, b);
		sort(yy.rbegin(), yy.rend());
		debug(yy);
		debug(ssize(prime_queries));
		debug(ssize(nearly_primes));
		debug(ssize(nearly_primes2));
		debug(ssize(can6));
		debug(ssize(can12));

		LL M = 1;
		vector<LL> values = {0};
		vector<vector<int>> seen(S), seen6(Q);
		vector<pair<int, int>> pairs;
		auto reduce = [](LL y, int p) {
			y %= p;
			y = -y;
			y += p;
			y %= p;
			return y;
		};

		REP(i, S) {
			const int p = primes[i];
			seen[i].resize(p);
			for (auto y : prime_queries) {
				y = reduce(y, p);
				seen[i][y] = true;
			}
		}
		REP(i, Q) {
			const int p = squares[i];
			seen6[i].resize(p);
			for (auto y : prime_queries) {
				y = reduce(y, p);
				seen6[i][y] = true;
			}
		}
		REP(i, S)
			debug(i, primes[i], seen[i]);

		vector<int> okay(S), okay6(Q);
		auto do_okay = [&] {
			REP(i, S) {
				const int p = primes[i];
				if (accumulate(seen[i].begin(), seen[i].end(), 0) == p - 1)
					okay[i] = true;
			}
			REP(i, Q) {
				const int p = squares[i];
				if (accumulate(seen6[i].begin(), seen6[i].end(), 0) >= p - int(sqrt(p)))
					okay6[i] = true;
			}
			debug(okay6, seen6);
		};

		auto do_qua = [&] {
			do_okay();
			vector<pair<int, int>> quasi_primes;
			REP(i, S) {
				if (not okay[i])
					continue;
				const int p = primes[i];
				debug(i, p);
				for (auto y : nearly_primes) {
					auto z = reduce(y, p);
					if (not seen[i][z]) {
						quasi_primes.emplace_back(y, p);
					}
				}
			}

			REP(i, Q) {
				if (not okay6[i])
					continue;
				const int p = squares[i];
				debug(i, p);
				for (auto y : can6) {
					auto z = reduce(y, p);
					if (not seen6[i][z]) {
						quasi_primes.emplace_back(y, int(sqrt(p)));
						debug("hurra");
					}
				}
			}

			debug(quasi_primes);
			REP(i, S) {
				const int p = primes[i];
				for (auto [y, forbidden_p] : quasi_primes) {
					if (p == forbidden_p)
						continue;
					y = reduce(y, p);
					seen[i][y] = true;
				}
			}
		};

		auto do_qua2 = [&] {
			do_okay();
			vector<tuple<int, int, int>> quasi_primes2;
			REP(i, S) {
				if (not okay[i])
					continue;
				const int p1 = primes[i];
				REP(j, i) {
					if (not okay[j])
						continue;
					const int p2 = primes[j];
					debug(i, p1, p2);
					for (auto y : nearly_primes2) {
						auto z1 = reduce(y, p1);
						auto z2 = reduce(y, p2);
						if (not seen[i][z1] and not seen[j][z2]) {
							quasi_primes2.emplace_back(y, p1, p2);
						}
					}
				}
			}
			REP(i, S) {
				if (not okay[i])
					continue;
				const int p1 = primes[i];
				REP(j, Q) {
					if (not okay6[j])
						continue;
					const int p2 = squares[j];
					if (p1 * p1 == p2)
						continue;
					debug(i, p1, p2);
					for (auto y : can12) {
						auto z1 = reduce(y, p1);
						auto z2 = reduce(y, p2);
						if (not seen[i][z1] and not seen6[j][z2]) {
							quasi_primes2.emplace_back(y, p1, int(sqrt(p2)));
						}
					}
				}
			}
			debug(quasi_primes2);
			REP(i, S) {
				const int p = primes[i];
				for (auto [y, f1, f2] : quasi_primes2) {
					if (p == f1 or p == f2)
						continue;
					y = reduce(y, p);
					seen[i][y] = true;
				}
			}
		};

		REP(i, 5) {
			do_qua();
			do_qua2();
		}

		REP(i, S) {
			int not_seen = 0;
			for (int x : seen[i])
				not_seen += not x;
			pairs.emplace_back(not_seen, -i);
		}

		sort(pairs.begin(), pairs.end());
		for (auto& [_, i] : pairs)
			i = -i;
		debug(pairs);

		for (auto [_, id] : pairs) {
			const int p = primes[id];
			const LL new_M = M * p;
			vector<LL> new_values;
			REP(i, p) {
				if (seen[id][i])
					continue;
				for (auto x : values) {
					auto temp = crt(x, M, i, p);
					if (temp <= n)
						new_values.emplace_back(temp);
				}
			}
			swap(values, new_values);
			debug(p, M, ssize(values));
			M = new_M;
			if (M > n)
				break;
		}
		debug(ssize(values));

		for (auto x : values) {
			if ([&] {
				for (auto [y, ans] : queries) {
					if (cnt_factors(x + y) != ans)
						return false;
				}
				return true;
			}()) {
				Answer(x);
				break;
			}
		}
	}
}

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#include "dzilib.h"
#include<bits/stdc++.h>
using namespace std;
using LL=long long;
#define FOR(i,l,r)for(int i=(l);i<=(r);++i)
#define REP(i,n)FOR(i,0,(n)-1)
#define ssize(x)int(x.size())
#ifdef DEBUG
auto operator<<(auto&o,auto x)->decltype(x.end(),o);
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<")";}
auto&operator<<(auto&o,tuple<auto,auto,auto,auto>t){return o<<"("<<get<0>(t)<<", "<<get<1>(t)<<", "<<get<2>(t)<<", "<<get<3>(t)<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif

namespace yosupo {
	uint64_t gcd_stein_impl( uint64_t x, uint64_t y ) {
    if( x == y ) { return x; }
    const uint64_t a = y - x;
    const uint64_t b = x - y;
    const int n = __builtin_ctzll( b );
    const uint64_t s = x < y ? a : b;
    const uint64_t t = x < y ? x : y;
    return gcd_stein_impl( s >> n, t );
}

uint64_t gcd_stein( uint64_t x, uint64_t y ) {
    if( x == 0 ) { return y; }
    if( y == 0 ) { return x; }
    const int n = __builtin_ctzll( x );
    const int m = __builtin_ctzll( y );
    return gcd_stein_impl( x >> n, y >> m ) << ( n < m ? n : m );
}

// ---- is_prime ----

uint64_t mod_pow( uint64_t x, uint64_t y, uint64_t mod ) {
    uint64_t ret = 1;
    uint64_t acc = x;
    for( ; y; y >>= 1 ) {
        if( y & 1 ) {
            ret = __uint128_t(ret) * acc % mod;
        }
        acc = __uint128_t(acc) * acc % mod;
    }
    return ret;
}

bool miller_rabin( uint64_t n, const std::initializer_list<uint64_t>& as ) {
    return std::all_of( as.begin(), as.end(), [n]( uint64_t a ) {
        if( n <= a ) { return true; }

        int e = __builtin_ctzll( n - 1 );
        uint64_t z = mod_pow( a, ( n - 1 ) >> e, n );
        if( z == 1 || z == n - 1 ) { return true; }

        while( --e ) {
            z = __uint128_t(z) * z % n;
            if( z == 1 ) { return false; }
            if( z == n - 1 ) { return true; }
        }

        return false;
    });
}

bool is_prime( uint64_t n ) {
    if( n == 2 ) { return true; }
    if( n % 2 == 0 ) { return false; }
    if( n < 4759123141 ) { return miller_rabin( n, { 2, 7, 61 } ); }
    return miller_rabin( n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 } );
}

// ---- Montgomery ----

class Montgomery {
    uint64_t mod;
    uint64_t R;
public:
    Montgomery( uint64_t n ) : mod(n), R(n) {
       for( size_t i = 0; i < 5; ++i ) {
          R *= 2 - mod * R;
       }
    }

    uint64_t fma( uint64_t a, uint64_t b, uint64_t c ) const {
        const __uint128_t d = __uint128_t(a) * b;
        const uint64_t    e = c + mod + ( d >> 64 );
        const uint64_t    f = uint64_t(d) * R;
        const uint64_t    g = ( __uint128_t(f) * mod ) >> 64;
        return e - g;
    }

    uint64_t mul( uint64_t a, uint64_t b ) const {
        return fma( a, b, 0 );
    }
};

// ---- Pollard's rho algorithm ----

uint64_t pollard_rho( uint64_t n ) {
    if( n % 2 == 0 ) { return 2; }
    const Montgomery m( n );

    constexpr uint64_t C1 = 1;
    constexpr uint64_t C2 = 2;
    constexpr uint64_t M = 512;

    uint64_t Z1 = 1;
    uint64_t Z2 = 2;
retry:
    uint64_t z1 = Z1;
    uint64_t z2 = Z2;
    for( size_t k = M; ; k *= 2 ) {
        const uint64_t x1 = z1 + n;
        const uint64_t x2 = z2 + n;
        for( size_t j = 0; j < k; j += M ) {
            const uint64_t y1 = z1;
            const uint64_t y2 = z2;

            uint64_t q1 = 1;
            uint64_t q2 = 2;
            z1 = m.fma( z1, z1, C1 );
            z2 = m.fma( z2, z2, C2 );
            for( size_t i = 0; i < M; ++i ) {
                const uint64_t t1 = x1 - z1;
                const uint64_t t2 = x2 - z2;
                z1 = m.fma( z1, z1, C1 );
                z2 = m.fma( z2, z2, C2 );
                q1 = m.mul( q1, t1 );
                q2 = m.mul( q2, t2 );
            }
            q1 = m.mul( q1, x1 - z1 );
            q2 = m.mul( q2, x2 - z2 );

            const uint64_t q3 = m.mul( q1, q2 );
            const uint64_t g3 = gcd_stein( n, q3 );
            if( g3 == 1 ) { continue; }
            if( g3 != n ) { return g3; }

            const uint64_t g1 = gcd_stein( n, q1 );
            const uint64_t g2 = gcd_stein( n, q2 );

            const uint64_t C = g1 != 1 ? C1 : C2;
            const uint64_t x = g1 != 1 ? x1 : x2;
            uint64_t       z = g1 != 1 ? y1 : y2;
            uint64_t       g = g1 != 1 ? g1 : g2;

            if( g == n ) {
                do {
                    z = m.fma( z, z, C );
                    g = gcd_stein( n, x - z );
                } while( g == 1 );
            }
            if( g != n ) {
                return g;
            }

            Z1 += 2;
            Z2 += 2;
            goto retry;
        }
    }
}

void factorize_impl( uint64_t n, std::vector<uint64_t>& ret ) {
    if( n <= 1 ) { return; }
    if( is_prime( n ) ) { ret.push_back( n ); return; }

    const uint64_t p = pollard_rho( n );

    factorize_impl( p, ret );
    factorize_impl( n / p, ret );
}

std::vector<uint64_t> factorize( uint64_t n ) {
    std::vector<uint64_t> ret;
    factorize_impl( n, ret );
    std::sort( ret.begin(), ret.end() );
    return ret;
}

}


tuple<LL, LL, LL> extended_gcd(LL a, LL b) {
	if(a == 0)
		return {b, 0, 1};
	auto [gcd, x, y] = extended_gcd(b % a, a);
	return {gcd, y - x * (b / a), x};
}
LL crt(LL a, LL m, LL b, LL n) {
	if(n > m) swap(a, b), swap(m, n);
	auto [d, x, y] = extended_gcd(m, n);
	assert((a - b) % d == 0);
	LL ret = (b - a) % n * x % n / d * m + a;
	return ret < 0 ? ret + m * n / d : ret;
}

mt19937_64 rng_64(0);
LL rd(LL l, LL r) {
	return uniform_int_distribution<LL>(l, r)(rng_64);
}

namespace acmlib {

vector<bool> comp;
vector<int> primes;
void sieve(int n) {
	primes.clear();
	comp.resize(n + 1);
	FOR(i, 2, n) {
		if (!comp[i]) primes.emplace_back(i);
		for (int p : primes) {
			int x = i * p;
			if (x > n) break;
			comp[x] = true;
			if (i % p == 0) break;
		}
	}
}

} // acmlib

struct Sieve {
	LL l, r;
	vector<LL> val, cnt;
	Sieve(LL n) : l(-1), r(-1) {
		const int s = int(sqrt(n) + 10);
		acmlib::sieve(s);
	}
	void sieve(LL _l, LL _r) {
		l = max(1ll, _l);
		r = _r;
		assert(l <= r);
		const int len = int(r - l + 1);
		val.resize(len);
		iota(val.begin(), val.end(), l);
		cnt.resize(len);
		fill(cnt.begin(), cnt.end(), 1);
		for (int p : acmlib::primes) {
			for (LL n = (l + p - 1) / p * p; n <= r; n += p) {
				int cur = 1;
				while (val[n - l] % p == 0) {
					++cur;
					val[n - l] /= p;
				}
				cnt[n - l] *= cur;
			}
		}
		REP(i, len) {
			if (val[i] > 1)
				cnt[i] *= 2;
		}
	}
	LL operator()(LL n) {
		assert(n >= l and n <= r);
		return cnt[n - l];
	}
};

LL llmul(LL a, LL b, LL m) {
	return LL(__int128_t(a) * b % m);
}
LL llpowi(LL a, LL n, LL m) {
	for (LL ret = 1;; n /= 2) {
		if (n == 0)
			return ret;
		if (n % 2)
			ret = llmul(ret, a, m);
		a = llmul(a, a, m);
	}
}
bool miller_rabin(LL n) {
	if(n < 2) return false;
	int r = 0;
	LL d = n - 1;
	while(d % 2 == 0)
		d /= 2, r++;
	for(int a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
		if (a % n == 0) continue;
		LL x = llpowi(a, d, n);
		if(x == 1 || x == n - 1)
			continue;
		bool composite = true;
		REP(i, r - 1) {
			x = llmul(x, x, n);
			if(x == n - 1) {
				composite = false;
				break;
			}
		}
		if(composite) return false;
	}
	return true;
}
// BEGIN HASH
LL rho_pollard(LL n) {
	if(n % 2 == 0) return 2;
	for(LL i = 1;; i++) {
		auto f = [&](LL x) { return (llmul(x, x, n) + i) % n; };
		LL x = 2, y = f(x), p;
		while((p = __gcd(n - x + y, n)) == 1)
			x = f(x), y = f(f(y));
		if(p != n) return p;
	}
}
vector<LL> factor(LL n) {
	if(n == 1) return {};
	if(miller_rabin(n)) return {n};
	LL x = rho_pollard(n);
	auto l = factor(x), r = factor(n / x);
	l.insert(l.end(), r.begin(), r.end());
	return l;
} // END HASH
vector<pair<LL, int>> get_pairs(LL n) {
	/*
	auto v = factor(n);
	sort(v.begin(), v.end());
	*/
	auto v = yosupo::factorize(n);
	vector<pair<LL, int>> ret;
	REP(i, ssize(v)) {
		int x = i + 1;
		while (x < ssize(v) and v[x] == v[i])
			++x;
		ret.emplace_back(v[i], x - i);
		i = x - 1;
	}
	return ret;
}
int cnt_factors(LL n) {
	int ret = 1;
	for (auto [_, x] : get_pairs(n))
		ret *= x + 1;
	return ret;
}
vector<LL> all_factors(LL n) {
	auto v = get_pairs(n);
	vector<LL> ret;
	function<void(LL,int)> gen = [&](LL val, int p) {
		if (p == ssize(v)) {
			ret.emplace_back(val);
			return;
		}
		auto [x, cnt] = v[p];
		gen(val, p + 1);
		REP(i, cnt) {
			val *= x;
			gen(val, p + 1);
		}
	};
	gen(1, 0);
	return ret;
}

int main() {
	cin.tie(0)->sync_with_stdio(0);

	const int t = GetT();
	const int q = GetQ();
	const int limit = q / t;
	const LL n = GetN();
	debug(t, q, limit, n);

	Sieve s(10 * n);

	const int sub2 = int(1e6);
	const int sub3 = int(1e9);

	if (n <= sub2) {
		s.sieve(1, 3 * n);
		REP(tt, t) {
			vector<pair<LL, LL>> queries(limit);
			for (auto& [y, ans] : queries) {
				y = rd(0, n);
				ans = Ask(y);
			}
			auto ok = [&](int x) {
				for (auto [y, ans] : queries) {
					if (s(x + y) != ans) {
						return false;
					}
				}
				return true;
			};
			bool found = false;
			FOR(x, 1, n) {
				if (ok(x)) {
					Answer(x);
					found = true;
					break;
				}
			}
			assert(found);
		}
		return 0;
	}

	if (n == sub3) {
		const int query_range = n;
		const int L = n + query_range;
		acmlib::sieve(1e6);
		const auto primes = acmlib::primes;
		REP(tt, t) {
			vector<pair<LL, LL>> queries(limit);
			for (auto& [y, ans] : queries) {
				y = rd(0, query_range);
				ans = Ask(y);
			}
			auto ok = [&](LL x) {
				if (x < 1 or x > n)
					return false;
				for (auto [y, ans] : queries) {
					if (cnt_factors(x + y) != ans) {
						return false;
					}
				}
				return true;
			};

			pair<LL, LL> best;
			for (auto [y, ans] : queries)
				best = max(best, pair(ans, y));
			const auto [val, y] = best;
			debug(val, y);

			bool found = false;
			vector<int> exponents;
			function<void(LL)> rec = [&](LL left) {
				if (left == 1) {
					function<void(LL, int, int)> gen = [&](LL x, int id_expo, int id_prime) {
						if (id_expo == ssize(exponents)) {
							if (ok(x - y)) {
								debug(x - y);
								Answer(x - y);
								found = true;
							}
							return;
						}
						LL lower_bound = x;
						FOR(i, id_expo, ssize(exponents) - 1) {
							REP(j, exponents[i]) {
								lower_bound *= primes[id_prime + i - id_expo];
								if (lower_bound > L)
									return;
							}
						}
						FOR(i, id_prime, ssize(primes)) {
							LL cur = x;
							REP(j, exponents[id_expo]) {
								cur *= primes[i];
								if (cur > L)
									return;
							}
							gen(cur, id_expo + 1, i + 1);
							if (found)
								return;
						}
					};
					gen(1, 0, 0);
					return;
				}
				for (auto f : all_factors(left)) {
					if (f == 1)
						continue;
					exponents.emplace_back(f - 1);
					rec(left / f);
					exponents.pop_back();
				}
			};
			rec(val);
			assert(found);
		}
		return 0;
	}

	acmlib::sieve(100);
	const auto primes = acmlib::primes;
	const vector<int> squares = {4, 9};
	const int S = ssize(primes);
	const int Q = ssize(squares);

	REP(tt, t) {
		const LL q_min = 1e8;
		const LL q_max = 1e9;

		vector<pair<LL, LL>> queries(limit);
		int hura = 0;
		vector<int> prime_queries;
		vector<int> nearly_primes;
		vector<int> nearly_primes2, can6, can12;
		map<int, int> hh;
		for (auto& [y, ans] : queries) {
			y = rd(q_min, q_max);
			ans = Ask(y);
			if (ans == 2) {
				prime_queries.emplace_back(y);
			}
			if (ans == 4) {
				nearly_primes.emplace_back(y);
			}
			if (ans == 8) {
				nearly_primes2.emplace_back(y);
			}
			if (ans == 6) {
				can6.emplace_back(y);
			}
			if (ans == 12) {
				can12.emplace_back(y);
			}
			hh[ans]++;
		}
		vector<pair<int, int>> yy(hh.begin(), hh.end());
		for (auto& [a, b] : yy)
			swap(a, b);
		sort(yy.rbegin(), yy.rend());
		debug(yy);
		debug(ssize(prime_queries));
		debug(ssize(nearly_primes));
		debug(ssize(nearly_primes2));
		debug(ssize(can6));
		debug(ssize(can12));

		LL M = 1;
		vector<LL> values = {0};
		vector<vector<int>> seen(S), seen6(Q);
		vector<pair<int, int>> pairs;
		auto reduce = [](LL y, int p) {
			y %= p;
			y = -y;
			y += p;
			y %= p;
			return y;
		};

		REP(i, S) {
			const int p = primes[i];
			seen[i].resize(p);
			for (auto y : prime_queries) {
				y = reduce(y, p);
				seen[i][y] = true;
			}
		}
		REP(i, Q) {
			const int p = squares[i];
			seen6[i].resize(p);
			for (auto y : prime_queries) {
				y = reduce(y, p);
				seen6[i][y] = true;
			}
		}
		REP(i, S)
			debug(i, primes[i], seen[i]);

		vector<int> okay(S), okay6(Q);
		auto do_okay = [&] {
			REP(i, S) {
				const int p = primes[i];
				if (accumulate(seen[i].begin(), seen[i].end(), 0) == p - 1)
					okay[i] = true;
			}
			REP(i, Q) {
				const int p = squares[i];
				if (accumulate(seen6[i].begin(), seen6[i].end(), 0) >= p - int(sqrt(p)))
					okay6[i] = true;
			}
			debug(okay6, seen6);
		};

		auto do_qua = [&] {
			do_okay();
			vector<pair<int, int>> quasi_primes;
			REP(i, S) {
				if (not okay[i])
					continue;
				const int p = primes[i];
				debug(i, p);
				for (auto y : nearly_primes) {
					auto z = reduce(y, p);
					if (not seen[i][z]) {
						quasi_primes.emplace_back(y, p);
					}
				}
			}

			REP(i, Q) {
				if (not okay6[i])
					continue;
				const int p = squares[i];
				debug(i, p);
				for (auto y : can6) {
					auto z = reduce(y, p);
					if (not seen6[i][z]) {
						quasi_primes.emplace_back(y, int(sqrt(p)));
						debug("hurra");
					}
				}
			}

			debug(quasi_primes);
			REP(i, S) {
				const int p = primes[i];
				for (auto [y, forbidden_p] : quasi_primes) {
					if (p == forbidden_p)
						continue;
					y = reduce(y, p);
					seen[i][y] = true;
				}
			}
		};

		auto do_qua2 = [&] {
			do_okay();
			vector<tuple<int, int, int>> quasi_primes2;
			REP(i, S) {
				if (not okay[i])
					continue;
				const int p1 = primes[i];
				REP(j, i) {
					if (not okay[j])
						continue;
					const int p2 = primes[j];
					debug(i, p1, p2);
					for (auto y : nearly_primes2) {
						auto z1 = reduce(y, p1);
						auto z2 = reduce(y, p2);
						if (not seen[i][z1] and not seen[j][z2]) {
							quasi_primes2.emplace_back(y, p1, p2);
						}
					}
				}
			}
			REP(i, S) {
				if (not okay[i])
					continue;
				const int p1 = primes[i];
				REP(j, Q) {
					if (not okay6[j])
						continue;
					const int p2 = squares[j];
					if (p1 * p1 == p2)
						continue;
					debug(i, p1, p2);
					for (auto y : can12) {
						auto z1 = reduce(y, p1);
						auto z2 = reduce(y, p2);
						if (not seen[i][z1] and not seen6[j][z2]) {
							quasi_primes2.emplace_back(y, p1, int(sqrt(p2)));
						}
					}
				}
			}
			debug(quasi_primes2);
			REP(i, S) {
				const int p = primes[i];
				for (auto [y, f1, f2] : quasi_primes2) {
					if (p == f1 or p == f2)
						continue;
					y = reduce(y, p);
					seen[i][y] = true;
				}
			}
		};

		REP(i, 5) {
			do_qua();
			do_qua2();
		}

		REP(i, S) {
			int not_seen = 0;
			for (int x : seen[i])
				not_seen += not x;
			pairs.emplace_back(not_seen, -i);
		}

		sort(pairs.begin(), pairs.end());
		for (auto& [_, i] : pairs)
			i = -i;
		debug(pairs);

		for (auto [_, id] : pairs) {
			const int p = primes[id];
			const LL new_M = M * p;
			vector<LL> new_values;
			REP(i, p) {
				if (seen[id][i])
					continue;
				for (auto x : values) {
					auto temp = crt(x, M, i, p);
					if (temp <= n)
						new_values.emplace_back(temp);
				}
			}
			swap(values, new_values);
			debug(p, M, ssize(values));
			M = new_M;
			if (M > n)
				break;
		}
		debug(ssize(values));

		for (auto x : values) {
			if ([&] {
				for (auto [y, ans] : queries) {
					if (cnt_factors(x + y) != ans)
						return false;
				}
				return true;
			}()) {
				Answer(x);
				break;
			}
		}
	}
}