#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_CYAN = "\033[1;36m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif // https://hitonanode.github.io/cplib-cpp/number/factorize.hpp #include #include #include #include #include namespace SPRP { // http://miller-rabin.appspot.com/ const std::vector> bases{ {126401071349994536}, // < 291831 {336781006125, 9639812373923155}, // < 1050535501 (1e9) {2, 2570940, 211991001, 3749873356}, // < 47636622961201 (4e13) {2, 325, 9375, 28178, 450775, 9780504, 1795265022} // <= 2^64 }; inline int get_id(long long n) { if (n < 291831) { return 0; } else if (n < 1050535501) { return 1; } else if (n < 47636622961201) return 2; else { return 3; } } } // namespace SPRP // Miller-Rabin primality test // https://ja.wikipedia.org/wiki/%E3%83%9F%E3%83%A9%E3%83%BC%E2%80%93%E3%83%A9%E3%83%93%E3%83%B3%E7%B4%A0%E6%95%B0%E5%88%A4%E5%AE%9A%E6%B3%95 // Complexity: O(lg n) per query inline struct { long long modpow(__int128 x, __int128 n, long long mod) noexcept { __int128 ret = 1; for (x %= mod; n; x = x * x % mod, n >>= 1) ret = (n & 1) ? ret * x % mod : ret; return ret; } bool operator()(long long n) noexcept { if (n < 2) return false; if (n % 2 == 0) return n == 2; int s = __builtin_ctzll(n - 1); for (__int128 a : SPRP::bases[SPRP::get_id(n)]) { if (a % n == 0) continue; a = modpow(a, (n - 1) >> s, n); bool may_composite = true; if (a == 1) continue; for (int r = s; r--; a = a * a % n) { if (a == n - 1) may_composite = false; } if (may_composite) return false; } return true; } } is_prime; // https://hitonanode.github.io/cplib-cpp/random/rand_nondeterministic.hpp #include #include struct rand_int_ { using lint = long long; std::mt19937 mt; rand_int_() : mt(42) {} // rand_int_() : mt(std::chrono::steady_clock::now().time_since_epoch().count()) {} lint operator()(lint x) { return this->operator()(0, x); } // [0, x) lint operator()(lint l, lint r) { std::uniform_int_distribution d(l, r - 1); return d(mt); } } rnd; lint power(lint x, lint n, lint MOD) { lint ans = 1; while (n>0) { if (n & 1) (ans *= x) %= MOD; (x *= x) %= MOD; n >>= 1; } return ans; } // https://hitonanode.github.io/cplib-cpp/number/euler_totient_phi.hpp #include #include // Euler's totient function // Complexity: O(NlgN) std::vector euler_phi_table(int N) { std::vector ret(N + 1); std::iota(ret.begin(), ret.end(), 0); for (int p = 2; p <= N; p++) { if (ret[p] == p) { ret[p] = p - 1; for (int i = p * 2; i <= N; i += p) ret[i] = ret[i] / p * (p - 1); } } return ret; } // Euler's totient function // Complexity: O(sqrtN) // https://csacademy.com/contest/fii-code-2021-round-2/task/clown-fiesta/ // https://kopricky.github.io/code/Computation_Advanced/tetration.html template Int euler_phi(Int n) { Int ret = n; if (n % 2 == 0) { ret /= 2; do { n /= 2; } while (n % 2 == 0); } if (n % 3 == 0) { ret = ret / 3 * 2; do { n /= 3; } while (n % 3 == 0); } for (Int i = 5; i * i <= n; i += 4) { if (n % i == 0) { ret = ret / i * (i - 1); do { n /= i; } while (n % i == 0); } i += 2; if (n % i == 0) { ret = ret / i * (i - 1); do { n /= i; } while (n % i == 0); } } if (n != 1) ret = ret / n * (n - 1); return ret; } lint B_tmp = 2; lint Ask(lint i, int j) { cout << "? " << i << ' ' << j << endl; lint resp = 1 % B_tmp; // cin >> resp; REP(_, j) resp = resp * i % B_tmp; return resp; } int main() { auto Solve = [&](int N, int M, int L) -> lint { if (L == 0) return Ask(N, 1); if (L == 1) return Ask(N, M); if (M == 0 and L > 0) return Ask(N, 0); if (N == 0) return Ask(0, 1); lint gcd_b = 0; REP(_, 50) { int p = 4; while (!is_prime(p)) p = rnd(0.9e5, 1e9); // dbg(p); lint m = lint(p) * p - Ask(p, 2); gcd_b = gcd(gcd_b, m); } // dbg(gcd_b); lint ans = power(N, M * power(M, L - 1, euler_phi(gcd_b)), gcd_b); if (gcd_b == 1) ans = 0; return ans; }; const int U = 30; // FOR(N, 1, U) FOR(M, 1, U) FOR(L, 1, U) FOR(B, 1, U) { // B_tmp = B; // auto ans = Solve(N, M, L); // auto phi = euler_phi(B); // const lint e = power(M, L, phi); // auto ans2 = B == 1 ? 0 : power(N, e, B); // if (N == 0) { // if (M == 0 and L == 0) ans2 = 0; // else if (M) { // ans2 = 0; // } else if (L) { // ans2 = 1 % B; // } // } // if (ans != ans2) { // dbg(make_tuple(N, M, L, B, ans, ans2, phi, e)); // exit(1); // } // // REP(_, L) e = e * M % phi; // } int N, M, L; cin >> N >> M >> L; auto ans = Solve(N, N, L); cout << "! " << ans << '\n'; }