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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.NoSuchElementException;

public class Main {
	private static void solve() {
		int n = nei();
		int a = nei();
		int[] x = new int[n];
		for (int i = 0; i < n; i++) {
			x[i] = nei();
		}
		long[][][] dp = new long[n + 1][n + 1][2600];
		for (int i = 0; i < n; i++) {
			dp[i][0][0] = 1;
		}
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				for (int k = 0; k < 2500; k++) {
					dp[i + 1][j][k] = dp[i][j][k];
				}
			}
			for (int j = 0; j < n; j++) {
				for (int k = 0; k < 2500; k++) {
					dp[i + 1][j + 1][k + x[i]] += dp[i][j][k];
				}
			}
		}
		long sum = 0;
		for (int i = 1; i <= n; i++) {
			sum += dp[n][i][i * a];
		}
		out(sum);
	}

	static BigInteger combination(int a, int b, BigInteger mod) {
		BigInteger q = BigInteger.ONE;
		BigInteger p = BigInteger.ONE;
		for (int i = a - b + 1; i <= a; i++) {
			q = q.multiply(BigInteger.valueOf(i)).mod(mod);
		}
		for (int j = 1; j <= b; j++) {
			p = p.multiply(BigInteger.valueOf(j)).mod(mod);
		}
		return q.multiply(p.modInverse(mod)).mod(mod);
	}

	static int abs(int x) {
		return x < 0 ? -x : x;
	}

	static int gcd(int x, int y) {
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		int z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static void out(String val) {
		IO.out(val);
	}

	static void out(int val) {
		IO.out(String.valueOf(val));
	}

	static void out(long val) {
		IO.out(String.valueOf(val));
	}

	static void out(char val) {
		IO.out(String.valueOf(val));
	}

	static void out(float val) {
		IO.out(String.valueOf(val));
	}

	static void out(double val) {
		IO.out(String.valueOf(val));
	}

	static void out(boolean val) {
		IO.out(String.valueOf(val));
	}

	static String next() {
		return IO.next();
	}

	static int nei() {
		return IO.nextInt();
	}

	static long nel() {
		return IO.nextLong();
	}

	static int parseInt(String val) {
		return Integer.parseInt(val);
	}

	static int parseInt(char val) {
		return Integer.parseInt(String.valueOf(val));
	}

	static long parseLong(String val) {
		return Long.parseLong(val);
	}

	public static void main(String[] args) {
		solve();
		IO.flush();
	}
}

final class UnionFind {
	int[] data;

	UnionFind(int n) {
		data = new int[n];
		for (int i = 0; i < n; i++) {
			data[i] = -1;
		}
	}

	boolean union(int x, int y) {
		x = root(x);
		y = root(y);
		if (x == y)
			return false;
		if (data[y] < data[x]) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		data[x] += data[y];
		data[y] = x;
		return true;
	}

	boolean find(int x, int y) {
		return root(x) == root(y);
	}

	int root(int x) {
		return data[x] < 0 ? x : (data[x] = root(data[x]));
	}

	int size(int x) {
		return -data[root(x)];
	}
}

final class IO {
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out, false);
	private static final byte[] buffer = new byte[1024];
	private static int ptr = 0;
	private static int len = 0;

	private static boolean hasNextByte() {
		if (ptr < len)
			return true;
		ptr = 0;
		try {
			len = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		return len > 0;
	}

	private static int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	static boolean hasNext() {
		byte c;
		while (hasNextByte() && ((c = buffer[ptr]) < '!' || c > '~'))
			ptr++;
		return hasNextByte();
	}

	static String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b >= '!' && b <= '~') {
			sb.append((char) b);
			b = readByte();
		}
		return sb.toString();
	}

	static long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static int nextInt() {
		if (!hasNext())
			throw new NoSuchElementException();
		int n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			b = readByte();
		}
		if (b < '0' || '9' < b)
			throw new NumberFormatException();
		while (true) {
			if ('0' <= b && b <= '9')
				n = n * 10 + b - '0';
			else if (b == -1 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static void out(String val) {
		out.println(val);
	}

	static void flush() {
		out.flush();
	}
}