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 dp[55][55][5000];

int main(void){
	int N,A;
	cin >> N >> A;
	int x[N];
	for(int i=0;i<N;i++)cin >> x[i];
	dp[0][0][0]=1;
	//dp[i][j][k]はx[0]~x[i]までの中からj個選んだ時、k=Σx;
	for(int i=0;i<N;i++){
		for(int j=0;j<=i;j++){
			for(int k=0;k<=2501;k++){
				//x[i]を選ばなかった場合
				dp[i+1][j][k] += dp[i][j][k];
				//x[i]を選んだ場合
				dp[i+1][j+1][k+x[i]] += dp[i][j][k];
			}
		}
	}
	long long ans = 0;
	for(int i=1;i<=N;i++){
		ans += dp[N][i][A*i];
	}
	cout << ans << endl;
}