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 5005
#define LL long long
using namespace std;

const int C = 2500;
int N,A;
int x[MAXN];
LL dp[MAXN], temp[MAXN];

int main(){
	
	cin>>N>>A;
	
	dp[C] = 1;
	
	for(int i=1,x;i<=N;i++){
		cin>>x;
		x -= A;
		memcpy(temp, dp, sizeof(dp));
		
		for(int j=0;j<=2*C;j++){
			if(j+x>=0 && j+x<=2*C) temp[j] += dp[j+x];
		}
		memcpy(dp, temp, sizeof(temp));
	}
	
	cout<<dp[C] - 1<<endl;
	
	return 0;
}