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>
using namespace std;
typedef long long ll;
#define INF 1LL<<62
#define inf 1000000007

ll x[50],dp[51][51][2510];
int main() {
	ll n,a;
	cin>>n>>a;
	for(ll i=1;i<=n;i++){
		cin>>x[i];
	}
	dp[0][0][0]=1;
	ll ans=0;
	for(ll i=1;i<=n;i++){
		for(ll j=0;j<=i;j++){
			for(ll k=0;k<=2500;k++){
				if(k-x[i]>=0&&j-1!=-1){
					dp[i][j][k]+=dp[i-1][j-1][k-x[i]];
				}
				dp[i][j][k]+=dp[i-1][j][k];
				if(j*a==k&&i==n&&j!=0){
					ans+=dp[i][j][k];
				}
			}
		}
	}
	cout <<ans;
	// your code goes here
	return 0;
}