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;

int main() {
	int N, A, X[50], x, MAX;
	static long long DP[60][5000] = {};
	cin >> N >> A;
	MAX = A;
	for (int i = 0; i < N; i++) {
		cin >> x;
		X[i] = x - A;
		MAX = max(MAX, abs(X[i]));
	}
	DP[0][N * MAX] = 1;
	for (int i = 0; i < N; i++) {
		for (int j = 0; j <= 2 * N * MAX; j++) {
			if (j - X[i] < 0 || j - X[i] > 2 * N * MAX) DP[i + 1][j] = DP[i][j];
			else DP[i + 1][j] = DP[i][j] + DP[i][j - X[i]];
		}
	}
	cout << DP[N][N * MAX] - 1;
}