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)

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>

using namespace std;

using i64 = long long;
#define forn(a, e) for (i64 a = 0; a < (i64)(e); a++)
#define forr(a, s, e) for (i64 a = s; a < (i64)(e); a++)
#define fore(e, a) for (auto& e : a)

#ifdef LOCAL
#define logv(a) {cerr << #a << " = "; fore(e, a) {cerr << e << " ";} cerr << "\n";}
#define logvp(a) {cerr << #a << " = "; fore(e, a) {cerr << "(" << e.first << ", " << e.second << ") ";} cerr << "\n";}
#define logvv(a) {cerr << #a << " = \n"; fore(r, a) { fore(e, r) {cerr << e << " ";} cerr << "\n";} }
#define logvf(a, field) {cerr << #a"."#field << " = \n"; fore(e, a) { cerr << e.field << " ";} cerr << "\n"; }
#define logvff(a, f1, f2) {cerr << #a".{"#f1 << ", "#f2 << "} = \n"; fore(e, a) { cerr << "(" << e.f1 <<", " << e.f2 << ") ";} cerr << "\n"; }
#define logs(a) cerr << #a << " = " << (a) << "\n";
#define logss(a, b) cerr << #a << " = " << (a) << ", " << #b << " = " << (b) << "\n";
#define logp(a) cerr << #a << " = " << "(" << a.first << ", " << a.second << ")" << "\n";
#define cond(pred, stmt) if (pred) { stmt }
#else
#define logv(a)
#define logvp(a)
#define logvv(a)
#define logvf(a, field)
#define logvff(a, f1, f2)
#define logs(a)
#define logss(a, b)
#define logp(a)
#define cond(pred, stmt)
#endif

using iip = pair<int, int>;
using llp = pair<i64, i64>;
using ivec = vector<int>;
using llvec = vector<i64>;
using svec = vector<string>;
template<typename T> using vec = vector<T>;

template<typename T, typename Dim>
auto make_vec(T value, Dim dim) { return vector<T>(dim, value); }
template<typename T, typename Dim1, typename... Dim>
auto make_vec(T value, Dim1 dim1, Dim... dims) { return make_vec(make_vec(value, dims...), dim1); }

template<typename T>
bool uax(T& v, const T& newv) { if (v < newv) { v = newv; return true; } else return false; }
template<typename T>
bool uin(T& v, const T& newv) { if (v > newv) { v = newv; return true; } else return false; }

template<typename T>
istream& operator>>(istream& is, vector<T>& c) { for (auto& e : c) is >> e; return is; }
template<typename T, size_t N>
istream& operator>>(istream& is, array<T, N>& c) { for (auto& e : c) is >> e; return is; }

template<typename ...T>
istream& read(T&... args) { return (cin >> ... >> args); }

static mt19937 rande(123123);
template<typename T>
T rand_int(T from, T to) { uniform_int_distribution<T> distr(from, to); return distr(rande); }

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    rande.seed(chrono::steady_clock::now().time_since_epoch().count());

    int n, a;
    while (read(n, a)) {
        ivec x(n);
        read(x);
        i64 ans = 0;
        forr(c, 1, n + 1) {
            int m = a * c;
            auto dp = make_vec(0ll, c + 1, m + 1);
            dp[0][0] = 1;
            fore(xi, x)  {
                for (int i = c - 1; i >= 0; i--) {
                    forn(sum, m) if (sum + xi <= m){
                        dp[i + 1][sum + xi] += dp[i][sum];
                    }
                }
            }
            // logs(c);
            // logvv(dp);
            ans += dp[c][m];
        }
        cout << ans << endl;
    }
}