UVA1639Candy

//UVA1639Candy
#include<cstdio>
#include<cstring>
#include<cmath>
const int maxn = 200000;
long double F[maxn];
double solve(int n, double p) {
	long double ans = 0;
	for(int i = 1; i <= n; i++) {
		long double c = F[2 * n - i] - F[n] - F[n - i];//將組合數變成log形式 
		long double v1 = c + (n + 1) * log(p) + (n - i) * log(1 - p);
		long double v2 = c + (n + 1) * log(1 - p) + (n - i) * log(p);
		ans += i * (exp(v1) + exp(v2));
	}
	return ans;
}
int main() {
	F[0] = 0;
	for(int i = 1; i <= maxn; i++) F[i] = F[i - 1] + log(i);
	int kase = 0, n;
	double p; 
	while(scanf("%d%lf", &n, &p) == 2) {
		printf("Case %d: %lf\n", ++kase, solve(n, p));
	}
	return 0;
}
/*
10 0.400000
100 0.500000
124 0.432650
325 0.325100
532 0.487520
2276 0.720000
*/