#include #include #include #include #include #include #include #include #include #include #include static const int MOD = 1000000007; using ll = long long; using u32 = unsigned; using u64 = unsigned long long; using namespace std; template constexpr T INF = ::numeric_limits::max()/32*15+208; #include using u64 = unsigned long long; using u128 = __uint128_t; template< class T> T pow_ (T x, u64 n, u64 M){ T u = 1; if(n > 0){ u = pow_(x, n/2, M); if (n % 2 == 0) u = (u*u) % M; else u = (((u * u)% M) * x) % M; } return u; }; bool suspect(__uint128_t a, u64 s, u64 d, u64 n){ __uint128_t x = pow_(a, d, n); if (x == 1) return true; for (int r = 0; r < s; ++r) { if(x == n-1) return true; x = x * x % n; } return false; } template bool miller_rabin(T m){ u64 n = m; if (n <= 1 || (n > 2 && n % 2 == 0)) return false; u64 d = n - 1, s = 0; while (!(d&1)) {++s; d >>= 1;} vector v = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; if(n <= 4759123141LL) v = {2, 7, 61}; for (auto &&p : v) { if(p >= n) break; if(!suspect(p, s, d, n)) return false; } return true; } template struct ExactDiv { T t, i, val; ExactDiv() {} ExactDiv(T n) : t(T(-1) / n), i(mul_inv(n)) , val(n) {}; T mul_inv(T n) { T x = n; for (int i = 0; i < 5; ++i) x *= 2 - n * x; return x; } bool divide(T n) const { if(val == 2) return !(n & 1); return n * this->i <= this->t; } }; vector> get_prime(int n){ if(n <= 1) return vector>(); vector is_prime(n+1, true); vector> prime; is_prime[0] = is_prime[1] = false; for (int i = 2; i <= n; ++i) { if(is_prime[i]) prime.emplace_back(i); for (auto &&j : prime){ if(i*j.val > n) break; is_prime[i*j.val] = false; if(j.divide(i)) break; } } return prime; } const auto primes = get_prime(1000); random_device rng; struct mod64 { u64 n; static u64 mod, inv, r2; mod64() : n(0) {} mod64(u64 x) : n(init(x)) {} static u64 init(u64 w) { return reduce(u128(w) * r2); } static void set_mod(u64 m) { mod = inv = m; for (int i = 0; i < 5; ++i) inv *= 2 - inv * m; r2 = -u128(m) % m; } static u64 reduce(u128 x) { u64 y = u64(x >> 64) - u64((u128(u64(x) * inv) * mod) >> 64); return ll(y) < 0 ? y + mod : y; }; mod64& operator+=(mod64 x) { n += x.n - mod; if(ll(n) < 0) n += mod; return *this; } mod64 operator+(mod64 x) const { return mod64(*this) += x; } mod64& operator*=(mod64 x) { n = reduce(u128(n) * x.n); return *this; } mod64 operator*(mod64 x) const { return mod64(*this) *= x; } u64 val() const { return reduce(n); } }; u64 mod64::mod, mod64::inv, mod64::r2; template T pollard_rho2(T n) { uniform_int_distribution ra(1, n-1); mod64::set_mod(n); while(true){ u64 c_ = ra(rng), g = 1, r = 1, m = 500; while(c_ == n-2) c_ = ra(rng); mod64 y(ra(rng)), xx(0), c(c_), ys(0), q(1); while(g == 1){ xx.n = y.n; for (int i = 1; i <= r; ++i) { y *= y; y += c; } T k = 0; g = 1; while(k < r && g == 1){ for (int i = 1; i <= (m > (r-k) ? (r-k) : m); ++i) { ys.n = y.n; y *= y; y += c; u64 xxx = xx.val(), yyy = y.val(); q *= mod64(xxx > yyy ? xxx - yyy : yyy - xxx); } g = __gcd(q.val(), n); k += m; } r *= 2; } if(g == n) g = 1; while (g == 1){ ys *= ys; ys += c; u64 xxx = xx.val(), yyy = ys.val(); g = __gcd(xxx > yyy ? xxx - yyy : yyy - xxx, n); } if (g != n && miller_rabin(g)) return g; } } template vector prime_factor(T n, int d = 0){ vector a, res; if(!d) for (auto &&i : primes) { while (i.divide(n)){ res.emplace_back(i.val); n /= i.val; } } while(n != 1){ if(miller_rabin(n)){ a.emplace_back(n); break; } T x = pollard_rho2(n); n /= x; a.emplace_back(x); } for (auto &&i : a) { if (miller_rabin(i)) { res.emplace_back(i); } else { vector b = prime_factor(i, d + 1); for (auto &&j : b) res.emplace_back(j); } } sort(res.begin(),res.end()); return res; } int main() { ll n, m; cin >> n >> m; double val = 0; if(n <= 1000){ for (int i = 1; i <= n; ++i) { val += log10(i); } }else { val = log10(2*acos(-1)*n)/2 + n * log10(n/exp(1)); } auto pf = prime_factor(m); map mm; for (auto &&i : pf) mm[i]++; ll p = INF; for (auto &&i : mm) { ll x = 0, nn = n; while(nn){ x += nn/i.first; nn /= i.first; } p = min(p, x/i.second); } val -= (p)*log10(m); printf("%.10lfe%.0lf\n", pow(10, val-floor(val)), floor(val)); return 0; }