Problem:
Score : 300 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

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.

Sample Input 1

4 8
7 9 8 9

Sample Output 1

5

The following are the 5 ways to select cards such that the average is 8:

Select the 3-rd card.

Select the 1-st and 2-nd cards.

Select the 1-st and 4-th cards.

Select the 1-st, 2-nd and 3-rd cards.

Select the 1-st, 3-rd and 4-th cards.

Sample Input 2

3 8
6 6 9

Sample Output 2

0

Sample Input 3

8 5
3 6 2 8 7 6 5 9

Sample Output 3

19

Sample Input 4

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

Sample Output 4

8589934591

The answer may not fit into a 32-bit integer.

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define si(x) scanf("%d",&x)
#define sl(x) scanf("%lld",&x)
#define pi(x) printf("%d",x)
#define pl(x) printf("%lld",x)
#define pb push_back
#define mkp make_pair
#define fi first
#define se second
#define re register
#define rep(i,m,n) for(int i=m;i<=n;i++)
#define per(i,n,m) for(int i=m;i>=n;i--)
#define rrep(i,m,n) for(register int i=m;i<=n;i++)
#define rper(i,n,m) for(register int i=m;i>=n;i--)
const int N = 3e3 + 10;
const ll mod = 1e9 + 7;
ll cnt[60][N];
int x[N];
signed main(){
    int n,a;
    si(n);
    si(a);
    rep(i,1,n)si(x[i]);
    cnt[0][0]=1;
    rep(i,1,n){
        per(k,1,i)
        rep(j,x[i],2501){
            cnt[k][j]+=cnt[k-1][j-x[i]];
        }
    }
    ll res=0;
    rep(i,1,n) {
        res+=cnt[i][i*a];
    }
    pl(res);
    return 0;
}