// >>> TEMPLATES #include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll using pii = pair<int, int>; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define pb push_back #define eb emplace_back #define fst first #define snd second template <class Int> auto constexpr inf_ = numeric_limits<Int>::max()/2-1; auto constexpr INF32 = inf_<int32_t>; auto constexpr INF64 = inf_<int64_t>; auto constexpr INF = inf_<int>; #ifdef LOCAL #include "debug.hpp" #define oj_local(x, y) (y) #else #define dump(...) (void)(0) #define debug if (0) #define oj_local(x, y) (x) #endif template <class T, class Comp> struct pque : priority_queue<T, vector<T>, Comp> { vector<T> &data() { return this->c; } void clear() { this->c.clear(); } }; template <class T> using pque_max = pque<T, less<T>>; template <class T> using pque_min = pque<T, greater<T>>; template <class T, class = typename T::iterator, enable_if_t<!is_same<T, string>::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template <class T, size_t N, enable_if_t<!is_same<T, char>::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template <class T, class = decltype(begin(declval<T&>())), class = typename enable_if<!is_same<T, string>::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template <class T, class S> ostream& operator<<(ostream& os, pair<T, S> const& p) { return os << p.first << " " << p.second; } template <class T, class S> istream& operator>>(istream& is, pair<T, S>& p) { return is >> p.first >> p.second; } template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t) { bool f = true; apply([&](auto&&... x) { ((os << (f ? f = false, "" : " ") << x), ...); }, t); return os; } template <class... T> istream& operator>>(istream& is, tuple<T...>& t) { apply([&](auto&&... x) { ((is >> x), ...); }, t); return is; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template <class F> struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward<F>(f)) {} template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); } }; struct MakeFixPoint { template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); } }; #define def(name, ...) auto name = MakeFixPoint() | [&](auto &&name, __VA_ARGS__) template <class T, size_t d> struct vec_impl { using type = vector<typename vec_impl<T, d-1>::type>; template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T, d-1>::make_v(forward<U>(x)...)); } }; template <class T> struct vec_impl<T, 0> { using type = T; static type make_v(T const& x = {}) { return x; } }; template <class T, size_t d = 1> using vec = typename vec_impl<T, d>::type; template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T, d>::make_v(forward<Args>(args)...); } template <class T> void quit(T const& x) { cout << x << '\n'; exit(0); } template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template <class It> constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits<It>::value_type{}); } template <class T, class = decltype(begin(declval<T&>()))> constexpr auto min(T const& a) { return *min_element(begin(a), end(a)); } template <class T, class = decltype(begin(declval<T&>()))> constexpr auto max(T const& a) { return *max_element(begin(a), end(a)); } template <class T> constexpr T min(set<T> const& st) { assert(st.size()); return *st.begin(); } template <class T> constexpr T max(set<T> const& st) { assert(st.size()); return *prev(st.end()); } template <class T> constexpr T min(multiset<T> const& st) { assert(st.size()); return *st.begin(); } template <class T> constexpr T max(multiset<T> const& st) { assert(st.size()); return *prev(st.end()); } constexpr ll max(signed x, ll y) { return max<ll>(x, y); } constexpr ll max(ll x, signed y) { return max<ll>(x, y); } constexpr ll min(signed x, ll y) { return min<ll>(x, y); } constexpr ll min(ll x, signed y) { return min<ll>(x, y); } template <class T> int sz(T const& x) { return x.size(); } template <class C, class T> int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template <class C, class T> int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr ll mod(ll x, ll m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr ll div_floor(ll x, ll y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr ll div_ceil(ll x, ll y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; auto four_nbd(int n, int m) { static vector<pair<int, int>> v; return [n, m](int i, int j) { const int dx[] = { 1, 0, -1, 0 }, dy[] = { 0, 1, 0, -1 }; v.clear(); rep (dir, 4) { int ni = i+dx[dir], nj = j+dy[dir]; if (0 <= ni and ni < n and 0 <= nj and nj < m) { v.emplace_back(ni, nj); } } return v; }; }; template <class Comp> vector<int> iota(int n, Comp comp) { vector<int> idx(n); iota(begin(idx), end(idx), 0); stable_sort(begin(idx), end(idx), comp); return idx; } constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template <class Int> Int rand(Int a, Int b) { return uniform_int_distribution<Int>(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand<i64>(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand<u64>(a, b); } // template <class It> void shuffle(It l, It r) { shuffle(l, r, seed_); } template <class V> V &operator--(V &v) { for (auto &x : v) --x; return v; } template <class V> V &operator++(V &v) { for (auto &x : v) ++x; return v; } bool next_product(vector<int> &v, int m) { repR (i, v.size()) if (++v[i] < m) return true; else v[i] = 0; return false; } bool next_product(vector<int> &v, vector<int> const& s) { repR (i, v.size()) if (++v[i] < s[i]) return true; else v[i] = 0; return false; } template <class vec> int sort_unique(vec &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); return v.size(); } template <class It> auto prefix_sum(It l, It r) { vector<typename It::value_type> s = { 0 }; while (l != r) s.emplace_back(s.back() + *l++); return s; } template <class It> auto suffix_sum(It l, It r) { vector<typename It::value_type> s = { 0 }; while (l != r) s.emplace_back(*--r + s.back()); reverse(s.begin(), s.end()); return s; } template <class T> T pop(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; } template <class T> T pop_back(vector<T> &a) { auto x = a.back(); a.pop_back(); return x; } template <class T, class V, class C> T pop(priority_queue<T, V, C> &a) { auto x = a.top(); a.pop(); return x; } template <class T> T pop(queue<T> &a) { auto x = a.front(); a.pop(); return x; } template <class T> T pop_front(deque<T> &a) { auto x = a.front(); a.pop_front(); return x; } template <class T> T pop_back(deque<T> &a) { auto x = a.back(); a.pop_back(); return x; } template <class T> T pop_front(set<T> &a) { auto x = *a.begin(); a.erase(a.begin()); return x; } template <class T> T pop_back(set<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } template <class T> T pop_front(multiset<T> &a) { auto it = a.begin(); auto x = *it; a.erase(it); return x; } template <class T> T pop_back(multiset<T> &a) { auto it = prev(a.end()); auto x = *it; a.erase(it); return x; } // <<< // >>> timer class Timer { chrono::system_clock::time_point t; public: Timer() { reset(); } void reset() { t = chrono::system_clock::now(); } double time() const { // milliseconds return chrono::duration_cast<chrono::microseconds>(chrono::system_clock::now()-t).count()/1000.0; } }; // <<< int32_t main() { int n, k; cin >> n >> k; auto win = [&]() { int A = 0, B = 0; rep (i, k) A += irand(4, 6); rep (i, n-k) A += irand(1, 6); rep (i, n) B += irand(1, 6); return A > B; }; int cnt = 0, total = 0; Timer t; while (t.time() < 4900) { rep (_, 1000) { cnt += win(); total++; } } cout << ld(cnt)/total << "\n"; cerr << total << '\n'; }