This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#define _CRT_SECURE_NO_WARNINGS
#include<stdio.h>
#include<math.h>
#include<algorithm>
using namespace std;
typedef long long ll;
ll C[50][50];
int main(){
int a, b, n;
ll K;
scanf("%d%d%d%lld", &a, &b, &n, &K);
C[0][0] = 1;
for (int i = 1; i <= 42; i++){
C[i][0] = 1;
for (int j = 1; j <= i; j++){
C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
}
}
ll now = 0;
if (a > b)swap(a, b);
for (int i = 0; i <= n; i++){
now += C[n][i];
if (now >= K){
printf("%.10f\n", log(a * b / 2.0) + 2 * (log(a) * i + log(b) * (n - i)) - n * log(a * a + b * b));
break;
}
}
return 0;
}
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