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 <iostream>
using namespace std;
int main(void){
    long long n,a,x[50],d[50][10000];
    cin>>n>>a;
    for(int i=0;i<n;i++){
        cin>>x[i];
        x[i]-=a;
        for(int j=0;j<10000;j++)d[i][j]=0;
    }
    d[0][5000]++;
    d[0][x[0]+5000]++;
    for(int i=1;i<n;i++){
        for(int j=-4000;j<4000;j++){
            d[i][j+5000]=d[i-1][j+5000]+d[i-1][j-x[i]+5000];
        }
    }
    cout<<d[n-1][5000]-1<<endl;
}
