#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef LOCAL #define eprintf(...) fprintf(stderr, __VA_ARGS__) #else #define eprintf(...) 42 #endif #define rep_(i, a_, b_, a, b, ...) for (int i = (a), i##_len = (b); i < i##_len; ++i) #define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define reprev_(i, a_, b_, a, b, ...) for (int i = (b-1), i##_min = (a); i >= i##_min; --i) #define reprev(i, ...) reprev_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define all(x) (x).begin(), (x).end() 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; } // template T gcd(T a, T b) { return b ? gcd(b, a % b) : a; } using namespace std; typedef long long ll; typedef unsigned long long ull; typedef pair P; typedef long double ld; constexpr int MOD = 1000000007; // + - * / ^ int mod(int a) { int res = a % MOD; if(res < 0) { return res + MOD; } return res; } int mul_mod(int a, int b) { ll res = ((ll)a * (ll)b) % MOD; return mod((int)res); } int pow_mod(int a, int b) { ll res = 1; while (b > 0) { if(b & 1) { res = res * (ll)a % (ll)MOD; } a = mul_mod(a, a); b >>= 1; } return (int)res; } int inv_mod(int a) { return pow_mod(a, MOD - 2); } int div_mod(int a, int b) { return mul_mod(a, inv_mod(b)); } // ! C constexpr int FAC_MAX = 3000001; ll fac[FAC_MAX], finv[FAC_MAX], inv[FAC_MAX]; void com_init() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < FAC_MAX; i++){ fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } ll com_mod(int a, int b){ if (a < b) return 0; if (a < 0 || b < 0) return 0; return fac[a] * (finv[b] * finv[a - b] % MOD) % MOD; } int main (void) { cin.tie(0); ios::sync_with_stdio(false); int n; cin >> n; ll ans = 1; for (int i = 1; i * i <= n; i++) { if (n % i != 0) continue; int j = n / i; ans = mul_mod(ans, pow_mod(i, j)); if (i == j) break; ans = mul_mod(ans, pow_mod(j, i)); } cout << ans << '\n'; return 0; }