#pragma GCC optimize ("O3") #pragma GCC target ("avx") #include #include #include #include #include #include #include #include #include #include #include #include #include #define getchar getchar_unlocked #define putchar putchar_unlocked #define _rep(_1, _2, _3, _4, name, ...) name #define rep2(i, n) rep3(i, 0, n) #define rep3(i, a, b) rep4(i, a, b, 1) #define rep4(i, a, b, c) for (int i = int(a); i < int(b); i += int(c)) #define rep(...) _rep(__VA_ARGS__, rep4, rep3, rep2, _)(__VA_ARGS__) using namespace std; using i8 = signed char; using i16 = signed short; using i64 = long long; using u8 = unsigned char; using u32 = unsigned; using u64 = unsigned long long; using f80 = long double; void solve() { const int N_MAX = 1e9; constexpr int sqrt_N = sqrt(N_MAX); static int smalls[sqrt_N + 1], larges[sqrt_N + 1]; static int primes[sqrt_N + 1]; int N; while (~scanf("%d", &N)) { double p; scanf("%lf", &p); int v = sqrt(N); rep(i, 1, v + 1) smalls[i] = i - 1, larges[i] = N / i - 1; rep(p, 2, v + 1) if (smalls[p] > smalls[p - 1]) { int q = p * p, pcnt = smalls[p - 1]; rep(i, 1, min(N / q, v) + 1) { int d = i * p; larges[i] -= ((d <= v) ? larges[d] : smalls[N / d]) - pcnt; } for (int i = v; i >= q; --i) smalls[i] -= smalls[i / p] - pcnt; } int prime_size = 0; rep(i, 2, v + 1) if (smalls[i] > smalls[i - 1]) { primes[prime_size++] = i; } primes[prime_size++] = v + 1; static double pows[2000] = {1}; rep(i, 1, 2000) pows[i] = pows[i - 1] * (1 - p); function< double(int, int, int) > rec = [&] (int n, int pi, int d) { double ret = 0.0; int t = ((n > v) ? larges[N / n] : smalls[n]) - smalls[primes[pi] - 1]; ret += pows[2 * (d - 1)] * t; rep(pj, pi, prime_size) { int pr = primes[pj]; if (pr * pr > n) break; for (int q = pr, nd = d * 2; i64(q) * pr <= n; q *= pr) { ret += rec(n / q, pj + 1, nd); nd += d; ret += pows[nd - 2]; } } return ret; }; double ans = rec(N, 0, 1); printf("%.12f\n", ans); } } int main() { auto beg = clock(); solve(); auto end = clock(); fprintf(stderr, "%.3f sec\n", double(end - beg) / CLOCKS_PER_SEC); }