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.io.*;
import java.util.*;


public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		Printer pr = new Printer(System.out);

		int n = sc.nextInt();
		int a = sc.nextInt();

		int[] x = new int[n];
		for (int i = 0; i < n; i++) {
			x[i] = sc.nextInt();
		}
		Arrays.sort(x);

		long[][][] dp = new long[n + 1][n + 1][a * n + 1];
//		for (int i = 0; i <= n; i++) {
//			Arrays.fill(dp[i], -1);
//		}
		dp[0][0][0] = 1;

		for (int i = 1; i <= n; i++) {
			for (int j = 0; j <= n; j++) {
				for (int k = 0; k <= j * a; k++) {
					dp[i][j][k] = dp[i - 1][j][k];
					if (k - x[i - 1] < 0 || j == 0) {
						continue;
					}
					dp[i][j][k] += dp[i - 1][j - 1][k - x[i - 1]];
				}
			}
		}

		long ret = 0;
		for (int i = 1; i <= n; i++) {
			ret += dp[n][i][i * a];
		}

		pr.println(ret);

		pr.close();
		sc.close();
	}

	private static class Printer extends PrintWriter {
		Printer(PrintStream out) {
			super(out);
		}
	}
}
