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>
#include<algorithm>
using namespace std;
long long mod=1000000007;
int c[110];
long long dp[110][11000];
int main(){
    int a,b;scanf("%d%d",&a,&b);
    for(int i=0;i<a;i++)scanf("%d",c+i);
    dp[0][0]=1;
    for(int i=0;i<a;i++){
        for(int j=i;j>=0;j--){
            for(int k=0;k+c[i]<11000;k++){
                dp[j+1][k+c[i]]=(dp[j+1][k+c[i]]+dp[j][k]);
            }
        }
    }
    long long ret=0;
    for(int i=1;i<=a;i++)ret=(ret+dp[i][i*b]);
    printf("%lld\n",ret);
}