#include #include using namespace atcoder; using namespace std; using ll = long long; // -------------------------------------------------------- template bool chmax(T &a, const T b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T &a, const T b) { if (b < a) { a = b; return 1; } return 0; } #define FOR(i, l, r) for (ll i = (l); i < (r); ++i) #define RFOR(i, l, r) for (ll i = (r) - 1; (l) <= i; --i) #define REP(i, n) FOR(i, 0, n) #define RREP(i, n) RFOR(i, 0, n) #define ALL(c) (c).begin(), (c).end() #define RALL(c) (c).rbegin(), (c).rend() #define SORT(c) sort(ALL(c)) #define RSORT(c) sort(RALL(c)) #define MIN(c) *min_element(ALL(c)) #define MAX(c) *max_element(ALL(c)) #define SUM(c) accumulate(ALL(c), 0LL) #define BITCNT(c) __builtin_popcountll(c) #define SZ(c) ((int)(c).size()) #define COUT(c) cout << (c) << '\n' #define debug(x) cerr << #x << " = " << (x) << '\n'; using P = pair; using VP = vector

; using VVP = vector; using VS = vector; using VI = vector; using VVI = vector; using VLL = vector; using VVLL = vector; using VB = vector; using VVB = vector; using VD = vector; using VVD = vector; static const double EPS = 1e-10; static const double PI = acos(-1.0); template void arrPrint(vector arr) { for (auto v : arr) cout << v << " "; cout << '\n'; } template void arrPrint2Dim(vector> arr) { for (auto a : arr) arrPrint(a); } template void arrPrintPair(vector> arr) { for (auto v : arr) cout << "{" << v.first << "," << v.second << "}, "; cout << '\n'; } const int dx[4] = {1, 0, -1, 0}; const int dy[4] = {0, 1, 0, -1}; ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; } ll lcm(ll a, ll b) { return a / gcd(a, b) * b; } // static const int INF = (1 << 30) - 1; // 1073741824 - 1 static const ll INF = (1LL << 62) - 1; // 4611686018427387904 - 1 ll llceil(ll a, ll b) { return (a + b - 1) / b; } using T = tuple; bool isPrime(ll n) { // is n prime or not if (n == 1) return false; for (ll i = 2; i * i <= n; i++) { if (n % i == 0) return false; } return true; } long long mod = 998244353; struct mint { public: long long x; mint(long long x = 0) : x((mod + x) % mod) {} mint(std::string &s) { long long z = 0; for (int i = 0; i < SZ(s); i++) { z *= 10; z += s[i] - '0'; z %= mod; } this->x = z; } mint &operator+=(const mint &a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint &operator-=(const mint &a) { if ((x += mod - a.x) >= mod) x -= mod; return *this; } mint operator-() const { mint res(*this); return res * -1; } mint &operator*=(const mint &a) { (x *= a.x) %= mod; return *this; } mint &operator/=(const mint &a) { long long n = mod - 2; mint u = 1, b = a; while (n > 0) { if (n & 1) { u *= b; } b *= b; n >>= 1; } return *this *= u; } mint operator+(const mint &a) const { mint res(*this); return res += a; } mint operator-(const mint &a) const { mint res(*this); return res -= a; } mint operator*(const mint &a) const { mint res(*this); return res *= a; } mint operator/(const mint &a) const { mint res(*this); return res /= a; } mint pow(ll t) const { if (!t) return 1; mint a = pow(t >> 1); a *= a; if (t & 1) a *= *this; return a; } friend std::ostream &operator<<(std::ostream &os, const mint &n) { return os << n.x; } bool operator==(const mint &a) const { return this->x == a.x; } bool operator<(const mint &r) { return this->x < r.x; } bool operator<=(const mint &r) { return this->x <= r.x; } bool operator!=(const mint &r) { return this->x != r.x; } }; int main() { cin.tie(0); ios::sync_with_stdio(false); const ll mi = 100, mx = 100000; ll A, B; map kToAns; auto labo = [&]() { RFOR(b, mi, mx + 1) { // if (!isPrime(b)) continue; mod = b; FOR(a, mi, mx + 1) { map gcdToNewX; bool ok = true; ll y = mint(a).pow(b).x; RFOR(x, mi, mx + 1) { ll k = gcd(x, y); mint newX = mint(x).pow(a); if (gcdToNewX.count(k) && gcdToNewX[k] != newX.x) { ok = false; break; } gcdToNewX[k] = newX.x; } if (ok) { A = a; B = b; kToAns = gcdToNewX; return; } } } }; labo(); // 実験結果より、これはいけるらしい mod = B; ll k, result; cout << A << " " << B << endl; cin >> k; cout << kToAns[k] << endl; cin >> result; }