Throwing Balls into the Baskets LightOJ - 1317

You probably have played the game “Throwing Balls into the Basket”. It is a simple game. You have to throw a ball into a basket from a certain distance. One day we (the AIUB ACMMER) were playing the game. But it was slightly different from the main game. In our game we were N people trying to throw balls into M identical Baskets. At each turn we all were selecting a basket and trying to throw a ball into it. After the game we saw exactly S balls were successful. Now you will be given the value of N and M. For each player probability of throwing a ball into any basket successfully is P. Assume that there are infinitely many balls and the probability of choosing a basket by any player is 1/M. If multiple people choose a common basket and throw their ball, you can assume that their balls will not conflict, and the probability remains same for getting inside a basket. You have to find the expected number of balls entered into the baskets after K turns.

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing three integers N (1 ≤ N ≤ 16), M (1 ≤ M ≤ 100) and K (0 ≤ K ≤ 100) and a real number P (0 ≤ P ≤ 1). P contains at most three places after the decimal point.

Output

For each case, print the case number and the expected number of balls. Errors less than 10-6 will be ignored.

Sample Input

2

1 1 1 0.5

1 1 2 0.5

Sample Output

Case 1: 0.5

Case 2: 1.000000

Think：与篮子无关，最终结果都是要投进去，直接求

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <iostream>
using namespace std;
int main(){
double n,m,k,p;
int t;
int tt=1;
scanf("%d",&t);
while(t--){
scanf("%lf%lf%lf%lf",&n,&m,&k,&p);
double sum=n*k*p;
printf("Case %d: %.10f\n",tt++,sum);
}
return 0;
}