Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i. He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A. In how many ways can he make his selection?

Constraints

* 1 \leq N \leq 50
* 1 \leq A \leq 50
* 1 \leq x_i \leq 50
* N,\,A,\,x_i are integers.

Input

The input is given from Standard Input in the following format:


N A
x_1 x_2 ... x_N


Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Examples

Input

4 8
7 9 8 9


Output

5


Input

3 8
6 6 9


Output

0


Input

8 5
3 6 2 8 7 6 5 9


Output

19


Input

33 3
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3


Output

8589934591
#include<bits/stdc++.h>
#define MAXN 55
#define MAXW 2505
#define INF 1000000000
using namespace std;
typedef long long ll;
int N,A,x[MAXN];
ll dp[MAXN][MAXW];
int main()
{
    scanf("%d%d",&N,&A);
    for(int i=1;i<=N;i++) scanf("%d",&x[i]);
    dp[0][0]=1;
    for(int i=1;i<=N;i++)
        for(int j=0;j<=2500;j++)
        {
            if(j>=A) dp[i][j]=dp[i-1][j-A]; else dp[i][j]=0;
            if(j>=x[i]) dp[i][j]+=dp[i-1][j-x[i]];
        }
    printf("%lld\n",dp[N][A*N]-1);
}
