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<iostream>
#include<math.h>
using namespace std;
int main(){
int a, b, N;
long long T, K;
cin >> a >> b >> N >> K;
if (a > b){
int t = a;
a = b;
b = t;
}
/*
double S = log(a*b/2);
a = a*a;
b = b*b;
double A = log((double)a / (double)(a + b));
double B = log((double)b / (double)(a + b));
T = 1;
for (int i = 0; i < N; i++){
T *= 2;
}
while (T > 1){
T = T / 2;
if (K<=T){
S += B;
}
else{
K = K - T;
S += A;
}
}
printf("%.10f\n", S);
*/
double S = (a*b) / 2;
double A = (double)(a*a) / ((a*a) + (b*b));
double B = (double)(b*b) / ((a*a) + (b*b));
T = 1;
for (int i = 0; i < N; i++){
T *= 2;
}
while (T > 1){
T = T / 2;
if (K <= T){
S = S * B;
}
else{
K = K - T;
S = S * A;
}
}
printf("%.10f\n", log(S));
return 0;
}
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