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<algorithm>
#include<vector>
#include<string>
#include<queue>
#define lol(i,n) for(int i=0;i<n;i++)
using namespace std;
long long dp[61][2511];
int main(){
	int n,k;
	cin>>n>>k;
	lol(i,n+1){
		lol(j,2501){
			dp[i][j]=0;
		}
	}dp[0][0]=1;
	lol(u,n){
		int a;cin>>a;
		for(int i=n-1;i>=0;i--){
			lol(j,2501){
				if(i+1<=n&&j+a<2501){
					dp[i+1][j+a]+=dp[i][j];
				}
			}
		}
	}
	long long ans=0;
	for(int i=1;i<=n;i++){
		ans+=dp[i][i*k];
	}
	cout<<ans<<endl;
	return 0;
}
