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>
typedef long long ll;

ll x[50], dp[51][51][2501];

int main() {
	ll n, a; scanf("%lld%lld", &n, &a);
	for (int i = 0; i < n; i++)scanf("%lld", &x[i]);
	dp[0][0][0] = 1;
	for (int i = 1; i <= n; i++) {
		for (int j = 0; j <= n; j++) {
			for (int k = 0; k <= 2500; k++) {
				dp[i][j][k] += dp[i - 1][j][k];
				if (j >= 1 && k >= x[i - 1])
					dp[i][j][k] += dp[i - 1][j - 1][k - x[i - 1]];
			}
		}
	}
	ll sum = 0;
	for (int i = 1; i <= n; i++)sum += dp[n][i][a*i];
	printf("%lld\n", sum);
}