#pragma GCC optimize("O3") #pragma GCC target("avx") #include #define rep(i ,n) for(int i=0;i<(int)(n);++i) #define repr(i ,n) for(int i=n;i>(int)(n);--i) #define rep1(i ,n) for(int i=1;i<=(int)(n);++i) #define ALL(a) a.begin(), a.end() #define RSORT(a) sort(ALL(a),greater<>()) #define SORT(a) sort(ALL(a)) #define bit_check(bit, i) ((bit>>(i)) & 1) #define PRINT(x) cout << x << endl; #define ENDL printf("\n"); using namespace std; typedef long long int i64; typedef unsigned long long u64; template using V = vector; using VI = V; const int INF = 2e9; const i64 MOD = 1e9 + 7; template inline bool chmin(T& a, T b){if(a>b){a=b; return true;} return false;} template inline bool chmax(T& a, T b){if(a> n >> k; long double ans = 0; for(long double i = 0.0 ; i <= n ; ++i){ for(int j = 0 ; j