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
import java.util.*;

public class Main{
  public static void main(String[]args){
    Scanner sc = new Scanner(System.in);
    String[] S = sc.nextLine().split(" ");
    int N = Integer.parseInt(S[0]);
    int A = Integer.parseInt(S[1]);
    
    int[] num = new int[N];
    int max = A;
    for(int i = 0; i < N; i++){
      num[i] = Integer.parseInt(sc.next());
      max = max < num[i] ? num[i] : max;
    }
    
    int M = N*max;
    long[][][] dp = new long[N+1][N+1][M+1];
    for(int i = 0; i <= N; i++){
      dp[i][0][0] = 1;
    }
    
    for(int i = 1; i <= N; i++){
      for(int j = 1; j <= i; j++){
        for(int k = 0; k <= M; k++){
          int z = num[i-1];
          if(z > k){
            dp[i][j][k] = dp[i-1][j][k];
          }else{
            dp[i][j][k] = dp[i-1][j][k] + dp[i-1][j-1][k-z];
          }
        }
      }
    }
    
    long ans = 0;
    for(int i = 1; i <= N; i++){
      ans += dp[N][i][i*A];
    }
    System.out.println(ans);
  }
}