Balls and Boxes

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 213    Accepted Submission(s): 157

Problem Description

Mr. Chopsticks is interested in random phenomena, and he conducts an experiment to study randomness. In the experiment, he throws n balls into m boxes in such a manner that each ball has equal probability of going to each boxes. After the experiment, he calculated the statistical variance V as

V=∑mi=1(Xi−X¯)2m

where Xi is the number of balls in the ith box, and X¯ is the average number of balls in a box.
Your task is to find out the expected value of V.

 

Input

The input contains multiple test cases. Each case contains two integers n and m (1 <= n, m <= 1000 000 000) in a line.
The input is terminated by n = m = 0.

 

Output

For each case, output the result as A/B in a line, where A/B should be an irreducible fraction. Let B=1 if the result is an integer.

 

Sample Input

2 12 20 0

 

Sample Output

0/11/2
规律题：（m-1）*n/(m*m);
#include<stdio.h>long long int gcd(long long int a,long long int b){    if(b==0)        return a;    else        return gcd(b,a%b);}int main(){   long long int n,m;    while(scanf("%lld%lld",&n,&m)!=-1)    {        if(n==0&&m==0)            break;        long long int sum=(m-1)*n;        long long int ni=m*m;        long long int we=gcd(sum,ni);        sum=sum/we;        ni=ni/we;        printf("%lld/%lld\n",sum,ni);    }}

Hint
In the second sample, there are four possible outcomes, two outcomes with V = 0 and two outcomes with V = 1.