#pragma region satashun //#pragma GCC optimize("Ofast") //#pragma GCC optimize("unroll-loops") #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using pii = pair; template using V = vector; template using VV = V>; template V make_vec(size_t a) { return V(a); } template auto make_vec(size_t a, Ts... ts) { return V(ts...))>(a, make_vec(ts...)); } #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i, n) rep2(i, 0, n) #define rep2(i, m, n) for (int i = m; i < (n); i++) #define per(i, b) per2(i, 0, b) #define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--) #define ALL(c) (c).begin(), (c).end() #define SZ(x) ((int)(x).size()) constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template void chmin(T& t, const U& u) { if (t > u) t = u; } template void chmax(T& t, const U& u) { if (t < u) t = u; } template void mkuni(vector& v) { sort(ALL(v)); v.erase(unique(ALL(v)), end(v)); } template vector sort_by(const vector& v, bool increasing = true) { vector res(v.size()); iota(res.begin(), res.end(), 0); if (increasing) { stable_sort(res.begin(), res.end(), [&](int i, int j) { return v[i] < v[j]; }); } else { stable_sort(res.begin(), res.end(), [&](int i, int j) { return v[i] > v[j]; }); } return res; } template istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template istream& operator>>(istream& is, vector& v) { for (auto& x : v) { is >> x; } return is; } template ostream& operator<<(ostream& os, const vector& v) { os << "{"; rep(i, v.size()) { if (i) os << ","; os << v[i]; } os << "}"; return os; } #ifdef LOCAL void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif template void scan(vector& v, T offset = T(0)) { for (auto& x : v) { cin >> x; x += offset; } } // suc : 1 = newline, 2 = space template void print(T x, int suc = 1) { cout << x; if (suc == 1) cout << "\n"; else if (suc == 2) cout << " "; } template void print(const vector& v, int suc = 1) { for (int i = 0; i < v.size(); ++i) print(v[i], i == int(v.size()) - 1 ? suc : 2); } template void show(T x) { print(x, 1); } template void show(Head H, Tail... T) { print(H, 2); show(T...); } struct prepare_io { prepare_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); } } prep_io; #pragma endregion satashun template T powmod(T x, U k, T m) { x %= m; T res = 1 % m; while (k) { if (k & 1) { res = res * x % m; } k >>= 1; x = x * x % m; } return res; } // see : https://joisino.hatenablog.com/entry/2017/08/03/210000 // see : https://misteer.hatenablog.com/entry/miller-rabin // test : https://yukicoder.me/problems/no/3030 // ref : http://miller-rabin.appspot.com/ // check if n is prime // n < 4,759,123,141 -> call miller_rabin // 2^64 > n >= 4,759,123,141 -> call miller_rabin_big // O(k log^3 n) bool miller_rabin(ll n) { static const vector v = {2, 7, 61}; if (n < 2) { return false; } else if (n == 2) { return true; } else if (n % 2 == 0) { return false; } ull d = n - 1; int s = 0; while (d % 2 == 0) { d /= 2; s++; } for (auto a : v) { if (a % n == 0) continue; auto x = powmod(a, d, n); if (x == 1 || x == n - 1) continue; rep(r, s) { auto y = x * x % n; if (y == 1) { if (x != 1 && x != n - 1) { return false; } else { x = 1; break; } } x = y; } if (x != 1) return false; } return true; } using R = __int128_t; using ull = unsigned long long; bool miller_rabin_big(ull n) { static const vector v = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; if (n < 2) { return false; } else if (n == 2) { return true; } else if (n % 2 == 0) { return false; } ull d = n - 1; int s = 0; while (d % 2 == 0) { d /= 2; s++; } for (auto a : v) { if (a % n == 0) continue; auto x = powmod(a, d, R(n)); if (x == 1 || x == n - 1) continue; rep(r, s) { auto y = x * x % n; if (y == 1) { if (x != 1 && x != n - 1) { return false; } else { x = 1; break; } } x = y; } if (x != 1) return false; } return true; } void slv() { V cand; for (ll i = 1; i <= 60; ++i) { ll pr = ((1ll << i) + 1); if (miller_rabin_big(pr)) { cand.pb(pr); } } show(cand); rep(mask, 1 << SZ(cand)) { ll p = 1; bool ok1 = 1; rep(j, SZ(cand)) if (mask >> j & 1) { if (TEN(18) / cand[j] < p) { ok1 = 0; break; } p *= cand[j]; } if (!ok1) continue; if ((p >= TEN(7) && p <= TEN(18))) { show(p); bool ok = 1; for (int a = 20; a <= 5000; ++a) { if (gcd(a * a - 398, p) != 1) { ok = 0; } } if (ok) { debug(p); } } } } int main() { int cases = 1; // cin >> cases; // rep(i, cases) slv(); show(16711935); show(1); return 0; }