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.Arrays;
import java.util.Scanner;

public class Main {
public static void main(String[] args) {
		
		Scanner keyboard = new Scanner(System.in); 
		
		int N = keyboard.nextInt();
		int A = keyboard.nextInt();
		int[] in = new int[N];
		for(int i=0; i < N; i++) {
			in[i] = keyboard.nextInt();
		}
		
		for (int i = 0; i < N; i++) {
			in[i] -= A;
		}
		
		long[][] masu = new long[51][5001];
		
		masu[0][2500] = 1;
		
		for(int j = 1; j < N+1; j++) {
			for(int k = 0; k < 5001; k++) {
				if(k-in[j-1] >= 0 && k-in[j-1] <= 5000) {
				masu[j][k] += masu[j-1][k-in[j-1]];
				masu[j][k] += masu[j-1][k];
				}
			}
		}
			
		System.out.println(masu[N][2500]-1);
		keyboard.close();
	}
}