/* Problem URL: https://codeforces.com/gym/102644/problem/A */ #include #include #include using namespace std; using namespace __gnu_pbds; template > using ordered_set = tree; #define V vector #define rmin(a, b) a = min(a, b) #define rmax(a, b) a = max(a, b) #define rep(i, lim) for (int i = 0; i < (lim); i++) #define nrep(i, s, lim) for (int i = s; i < (lim); i++) #define repv(i, v) for (auto &i : (v)) #define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; } #define sortv(v) sort(v.begin(), v.end()) #define all(v) (v).begin(), (v).end() using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using ll = long long; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; template auto operator<<(ostream &os, const vector &vec)->ostream& { os << vec[0]; for (size_t i = 1; i < vec.size(); i++) { os << ' ' << vec[i]; } os << '\n'; return os; } template auto operator>>(istream &is, vector &vec)->istream& { for (auto &i : vec) { is >> i; } return is; } template auto operator<<(ostream &os, const vector> &vec)->ostream& { for (auto &i : vec) { os << i[0]; for (size_t j = 1; j < i.size(); j++) { os << ' ' << i[j]; } os << '\n'; } return os; } template auto operator>>(istream &is, vector> &vec)->istream& { for (auto &i : vec) { for (auto &j : i) { is >> j; } } return is; } const int oo = INT32_MAX >> 1; const ll OO = INT64_MAX >> 1; void pre() { } #define TEST 0 void solve() { ll n; long double p; cin >> n >> p; // long double h = 1; // long double s = 1; // // rep(i, n) { // long double th = h * (1 - p) + s * p; // long double ts = h * p + s * (p - 1); // h = th; // s = ts; // } V> mat = {{1}, {0}}; auto mul = [&](V> &a, V> &b) { V> c(a.size(), V(b[0].size())); rep(i, c.size()) { rep(j, c[0].size()) { rep(k, b.size()) { c[i][j] += a[i][k] * b[k][j]; } } } return c; }; V> prob = {{1 - p, p}, {p, 1 - p}}; rep(i, 30) { if ((n >> i) & 1) { mat = mul(prob, mat); } prob = mul(prob, prob); } cout << fixed << setprecision(10) << mat[0][0] << '\n'; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); pre(); int t; (TEST && cin >> t) || (t = 1); while (t--) { solve(); } }