学步园

The 11th Zhejiang Provincial Collegiate Programming Contest is coming! As a problem setter, Edward is going to arrange the order of the problems. As we know, the arrangement will have
a great effect on the result of the contest. For example, it will take more time to finish the first problem if the easiest problem hides in the middle of the problem list.

There are N problems in the contest. Certainly, it's not interesting if the problems are sorted in the order of increasing difficulty. Edward decides to arrange the problems
in a different way. After a careful study, he found out that the i-th problem placed in the j-th position will add P_ij points of "interesting value" to the contest.

Edward wrote a program which can generate a random permutation of the problems. If the total interesting value of a permutation is larger than or equal to M points, the permutation
is acceptable. Edward wants to know the expected times of generation needed to obtain the first acceptable permutation.

Input

There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:

The first line contains two integers N (1 <= N <= 12) and M (1 <= M <= 500).

The next N lines, each line contains N integers. The j-th integer in the i-th line is P_ij (0 <= P_ij <= 100).

Output

For each test case, output the expected times in the form of irreducible fraction. An irreducible fraction is a fraction in which the numerator and denominator are positive integers and
have no other common divisors than 1. If it is impossible to get an acceptable permutation, output "No solution" instead.

Sample Input

2
3 10
2 4 1
3 2 2
4 5 3
2 6
1 3
2 4

Sample Output

3/1
No solution

#include<cstring>
#include<iostream>
#include<cstdio>
#include<vector>
#include<algorithm>
#include<cmath>
#include<queue>
#include<stack>
#include<string>
#include<cstdlib>
using namespace std;
#define re freopen("in.txt","r",stdin)
#define we freopen("out.txt","w",stdout)
#define maxn 511
#define maxm maxn*maxn/2
#define ll long long
#define ld long double


int ma[15][15];
int dp[1<<12][511];
int gcd(int a,int b)
{
    while(b){
        int t=a%b;
        a=b;
        b=t;
    }
    return a;
}
int main()
{
    int nc;
    re;
    scanf("%d",&nc);
    while(nc--){
        memset(dp,0,sizeof(dp));
        memset(ma,0,sizeof(ma));
        int n,m;
        scanf("%d%d",&n,&m);
        for(int i=0;i<n;i++)
            for(int j=0;j<n;j++)
            scanf("%d",&ma[i][j]);
        dp[0][0]=1;
        int all=1<<n;
        int cnt=0;
        for(int st=0;st<all;st++){
            cnt=0;
            for(int c=0;c<n;c++)
                if(st&(1<<c))cnt++;
            for(int c=0;c<=m;c++){
                if(dp[st][c]){
                    for(int j=0;j<n;j++)
                    if(!(st&(1<<j))){
                        dp[st|(1<<j)][min(m,c+ma[j][cnt])]+=dp[st][c];
                    }
                }
            }
        }
        int ans=dp[all-1][m];
        int b=1;
        for(int j=2;j<=n;j++)
            b*=j;
        int gc=gcd(ans,b);
        ans/=gc;
        b/=gc;
        if(ans)
            printf("%d/%d\n",b,ans);
        else puts("No solution");
    }
    return 0;
}