This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<stdio.h>
#include<algorithm>
#include<math.h>
long long pascal[41][41];
long long pow(long long n, long long k) {
if (k == 0) {
return 1;
}
long long temp = pow(n, k / 2);
if (k % 2 == 0) {
return temp*temp;
}
return temp*temp*n;
}
int main() {
for (int i = 0; i <= 40; i++) {
for (int j = 0; j <= i; j++) {
if (j == 0 || j == i) {
pascal[i][j] = 1;
}
else {
pascal[i][j] = pascal[i - 1][j] + pascal[i - 1][j - 1];
}
}
}
long long a, b, n, k;
scanf("%lld%lld%lld%lld", &a, &b, &n, &k);
if (a < b) {
std::swap(a, b);
}
long long l = pow(2, n);
double s = (double)a*b/2;
for (int i = 0; i <= n; i++) {
k -= pascal[n][i];
if (k <= 0) {
for (int j = 1; j <= i; j++) {
s = s*b*b / ((a*a) + (b*b));
}
for (int j = 1; j <= n-i; j++) {
s = s*a*a / ((a*a) + (b*b));
}
break;
}
}
printf("%.12lf", log(s));
}
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