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>
using namespace std;

int main() {
    int N,A;
    int x[50];
    cin >> N >> A;
    for(int i=0; i<N; ++i) {
        int tmp; cin >> tmp;
        x[i] = tmp - A;
    }
    long long dp[50][4901] = {0};
    dp[0][2450] = 1;
    dp[0][x[0] + 2450] += 1;
    for(int i=1; i<N; ++i) {
        for(int j=0; j<=4900; ++j) {
            dp[i][j] = dp[i-1][j];
            if(j-x[i] >= 0 && j-x[i] <= 4900) dp[i][j] += dp[i-1][j - x[i]];
        }
    }
    cout << dp[N-1][2450] - 1 << endl;
}