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>
#define MAXN 55
#define LL long long
using namespace std;
const int C = 2500;
int N,A;
int x[MAXN];
LL dp[MAXN][MAXN][C+5]; 

int main(){
	
	cin>>N>>A;
	
	for(int i=0;i<=N;i++) dp[i][0][0] = 1;
	for(int i=1,x;i<=N;i++){
		cin>>x;
		
		for(int j=1;j<=N;j++){
			for(int s=0;s<=C;s++){
				dp[i][j][s] = dp[i-1][j][s];
				if(s>=x) dp[i][j][s] += dp[i-1][j-1][s-x];
			}
		}
	}
	
	LL ans = 0;
	for(int j=1;j<=N;j++){
		ans += dp[N][j][j*A];
	}
	
	cout<<ans<<endl;
	
	return 0;
}