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
/*
解法が分からなかった（アイデアが分からなかった）

*/
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
#define rep(i, start, n) for (int i = start; i < (int)(n); i++)
typedef long long ll;
int N, A;
int x[50];
ll dp[51][51][3010];

int main() {
	cin >> N >> A;
	rep(i, 0, N) cin >> x[i];
 
	dp[0][0][0] = 1;
	rep(i, 0, N) rep(j, 0, N) rep(k, 0, 2500) if(dp[i][j][k]){
		dp[i + 1][j][k] += dp[i][j][k];
		dp[i + 1][j + 1][k + x[i]] += dp[i][j][k];
	}
 
	ll ans = 0;
	rep(i, 1, N + 1) ans += dp[N][i][i*A];
	cout << ans << endl;
}