#define _USE_MATH_DEFINES #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; void integerFactorization(long long n, vector >& factor) { factor.clear(); long long a = 2; while(a * a <= n){ int b = 0; while(n % a == 0){ ++ b; n /= a; } if(b > 0) factor.push_back(make_pair(a, b)); ++ a; } if(n > 1) factor.push_back(make_pair(n, 1)); } long long legendreFormula(long long n, long long a) { vector > factor; integerFactorization(a, factor); long long ans = LLONG_MAX; for(const auto& p : factor){ long long b = 1; long long cnt = 0; while(b <= n / p.first){ b *= p.first; cnt += n / b; } ans = min(ans, cnt / p.second); } return ans; } double stirlingApproximation(long long n) { double ans = 0.0; if(n <= 20){ // nが小さいと近似精度が低いため愚直に計算する for(int i=1; i<=n; ++i) ans += log(i); } else{ ans = log(2.0 * M_PI * n) / 2.0 + n * log(n / M_E) + log(1.0 + (1.0 / 12.0 + (1.0 / 288.0 - 139.0 / 51840.0 / n) / n) / n); } return ans; } int main() { long long n, m; cin >> n >> m; double a = stirlingApproximation(n); a -= legendreFormula(n, m) * log(m); a /= log(10); long long digit = (long long)a; a -= digit; a *= log(10); printf("%.10fe%lld\n", exp(a), digit); return 0; }