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<vector>
#include<string>
using namespace std;

#define FOR(k,m,n) for(int (k)=(m);(k)<(n);(k)++)
#define rep(i,n) FOR((i),0,(n))

typedef long long ll;

const int INF=1e9+7;
ll dp[51][2600];
int main(){
	int n,a;
	cin>>n>>a;
	dp[0][0]=1;
	rep(i,n){
		int x;
		cin>>x;
		for(int j=2560-x;j>=0;j--)for(int k=50;k>=1;k--)dp[k][j+x]+=dp[k-1][j];	
	}
	ll ans=0;
	for(int i=1;i<2550;i++)for(int j=1;j<51;j++)if(i==a*j)ans+=dp[j][i];
	cout<<ans<<endl;
}
