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>
#include <algorithm>
#include <queue>
#include <set>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)

using namespace std;
typedef long long int lli;

//dp[i][j]. 偶奇でi番目までで部分和j-2550になる通り数
lli dp[2][5100];

int main(){
	lli N,A;
	cin>>N>>A;
	lli x[50];
	rep(i,50){
		cin>>x[i];
		x[i]-=A;
	}
	dp[1][2550]=1;
	
	rep(i,N){
		lli t=(i&1);
		rep(j,5000) dp[t][j]=dp[t^1][j]+dp[t^1][j-x[i]];
	}
	
	cout<<dp[(N-1)&1][2550]-1;
}