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 ll = int_fast64_t;
#define REP(i,b,e) for(ll i=b; i<e; i++)

//i個目までみてj個選んだ時総和がkになる組み合わせ数
ll dp[60][60][3000] = {};

int main(){
	int n, x;
	scanf("%d %d", &n, &x);
	int a[n];
	REP(i, 0, n) scanf("%d", &a[i]);
	dp[0][0][0] = 1;

	REP(i, 0, n) REP(j, 0, 1+n) REP(k, 0, 2500) {
	    dp[i+1][j][k] += dp[i][j][k];
	    if(j<n) dp[i+1][j+1][k+a[i]] += dp[i][j][k];
	}
	
	ll ans = 0;
	REP(j, 1, n+1) {
	    ans += dp[n][j][x*j];
	}
	printf("%ld\n", ans);
	return 0;
}

