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 <iostream>
#include <algorithm>

using namespace std;
typedef long long ll;

const int MAX_N = 50;
const int MAX_A = 50;

ll dp[MAX_N+1][MAX_A*MAX_N*2];

int main() {
	int N, A, tmp;
	int card[MAX_N];
	cin >> N >> A;
	for(int i=0;i<N;i++) {
		cin >> tmp;
		card[i] = tmp - A;
	}
	dp[0][MAX_A*MAX_N] = 1;
	for(int i=0;i<N;i++) {
		for(int j=0;j<MAX_A*MAX_N*2;j++) {
			if(dp[i][j] == 0) continue; 
			dp[i+1][j+card[i]] += dp[i][j];
			dp[i+1][j] += dp[i][j];
		}
	}
	cout << dp[N][MAX_A*MAX_N]-1 << endl;

	return 0;
}
