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 int dp[51][51][2501];

int main() {
	long long int N,A;
	cin >> N >> A;
	int x[N];
	for(int i = 0;i < N;i++) {
		cin >> x[i];
	}
	long long ans = 0;
	dp[0][0][0] = 1;
	for (int i = 0;i < N;i++) {
		for (int j = 0;j < N;j++) {
			for (int k = 0;k < 2501;k++) {
				if (k<x[i]) {dp[i+1][j][k] = dp[i][j][k];}
				else {
					dp[i+1][j+1][k] = dp[i][j+1][k] + dp[i][j][k-x[i]];
				}
			}
		}
	}
	for (int i = 1;i < N+1;i++) {
		ans+=dp[N][i][i*A];
	}
	cout << ans << endl;
}