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>

using namespace std;

long long n, A, a[55], q[10005][55];

int main(){
    cin >> n >> A;
    for(long long i = 1; i <= n; i++){
        cin >> a[i];
        a[i] = a[i] - A;
    }
    for(long long j = 1; j <= n; j++){
        for(long long i = 0; i <= 6000; i++){
            long long tmp = i - a[j];
            if(tmp >= 0) q[i][j] = q[i][j - 1] + q[tmp][j - 1];
            if(i == a[j] + 2500) q[i][j] += 1;
        }
    }
    cout << q[2500][n];
}
