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 int long long
using namespace std;

const int geta = 3000;

signed main(){
	int N,A;
	cin>>N>>A;
	vector<int> x(N);
	for(int i=0;i<N;i++){
		cin >>x[i];
		x[i]-=A;
	}
	
	int dp[51][6000] ;
	for(int i=0;i<50;i++){
		for(int j=0;j<6000;j++){
			dp[i][j]=0;
		}
	}
	
	for(int i=0;i<N;i++){
		dp[i+1][x[i]+geta]++;
		for(int k=0;k<6000;k++){
			dp[i+1][k]+=dp[i][k];
			dp[i+1][k+x[i]]+=dp[i][k];
		}
	}
	
	cout<< dp[N][geta]<<endl;	
}

