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<stdio.h>
int n,k;
long long mem[55][2555];
int main()
{
    int i,x,y,val;
    long long ans;
    scanf("%d%d",&n,&k);
    mem[0][0] = 1;
    for(i=0;i<n;i++)
    {
        scanf("%d",&val);
        for(x=n;x>=0;x--)
        {
            for(y=0;y<=2500;y++)
            {
                if(mem[x][y]) mem[x+1][y+val] += mem[x][y];
            }
        }
    }
    ans = 0;
    for(i=1;i<=n;i++) ans += mem[i][k*i];
    printf("%lld",ans);
}
