#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define REP(i,s,n) for(int i=(int)(s);i<(int)(n);i++) using namespace std; typedef long long int ll; typedef vector VI; typedef vector VL; typedef pair PI; /** * For every prime factor p, perform result[p] += e. (where n = \prod p^e) * Verified by: Codeforces #400 E * (http://codeforces.com/contest/776/submission/24956471) */ void factorize(long long v, std::map &result) { long long p = 2; while (v > 1 && p * p <= v) { int cnt = 0; while (v % p == 0) { cnt++; v /= p; } if (cnt > 0) { if (result.count(p) == 0) { result[p] = 0; } result[p] += cnt; } p += p == 2 ? 1 : 2; } if (v > 1) { if (result.count(v) == 0) { result[v] = 0; } result[v] += 1; } } const ll THRESHOLD = 100000; int main(void) { ios::sync_with_stdio(false); cin.tie(0); ll n, m; cin >> n >> m; map fact; factorize(m, fact); ll mi = 1e16; for (auto v: fact) { ll p = v.first; int e = v.second; ll einn = 0; ll k = n; while (k > 0) { k /= p; einn += k; } mi = min(mi, einn / e); } double ret = 0; if (n < THRESHOLD) { REP(i, 1, n + 1) { ret += log10(i); } } else { // Stirling's approximation ret = n * (log10(n / exp(1)) + log10(n * sinh(1.0 / n) + 1.0 / (810.0 * pow(n, 6))) / 2.0); ret += log10(2 * acos(-1) * n) / 2.0; } ret -= mi * log10(m); ll tenexp = floor(ret); ret -= tenexp; ret = pow(10, ret); cout << ret << "e" << tenexp << "\n"; }