Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np


def main(n, a, x):
    SUM_MAX = max(a, max(x)) * n + 1
    dp = np.zeros(shape=(n + 1, n + 1, SUM_MAX), dtype=int)

    dp[0][0][0] = 1
    for j in range(1, n + 1):
        for k in range(j + 1):
            for s in range(SUM_MAX):
                if s < x[j - 1]:
                    dp[j][k][s] = dp[j - 1][k][s]
                elif k >= 1:
                    dp[j][k][s] = dp[j - 1][k][s] + dp[j - 1][k - 1][s - x[j - 1]]

    patterns = 0
    for k in range(1, n + 1):
        ka = k * a
        patterns += dp[n][k][ka]
    return patterns


if __name__ == '__main__':
    N, A = map(int, input().split())
    X = list(map(int, input().split()))
    print(main(N, A, X))


Fixed submission:
import numpy as np


def main(n, a, x):
    SUM_MAX = max(a, max(x)) * n + 1
    dp = np.zeros(shape=(n + 1, n + 1, SUM_MAX), dtype=int)

    dp[0][0][0] = 1
    for j in range(1, n + 1):
        for k in range(j + 1):
            dp[j][k][0:x[j - 1]] = dp[j - 1][k][0:x[j - 1]]
            if k >= 1:
                dp[j][k][x[j - 1]:] = dp[j - 1][k][x[j - 1]:] + dp[j - 1][k - 1][:SUM_MAX - x[j - 1]]

    patterns = 0
    for k in range(1, n + 1):
        ka = k * a
        patterns += dp[n][k][ka]
    return patterns


if __name__ == '__main__':
    N, A = map(int, input().split())
    X = list(map(int, input().split()))
    print(main(N, A, X))

Buggy python submission (verdict: Time Limit Exceeded):
import math


class DFS:
    def __init__(self, average, numbers):
        self.average = average
        self.numbers = sorted([n for n in numbers if n != average], reverse=True)
        self.length = len(self.numbers)
        self.sum = average * self.length
        self.pre_patterns = int(math.pow(2, numbers.count(self.average))) - 1

    def _dfs(self, index, sum, picked):
        patterns = 0
        sum_if_added = sum + self.numbers[index]
        sum_if_not_added = sum
        picked_if_added = picked + 1
        picked_if_not_added = picked
        if index == self.length - 1:
            if self.average == sum_if_added / picked_if_added:
                patterns += 1
            if picked_if_not_added != 0 and self.average == sum_if_not_added / picked_if_not_added:
                patterns += 1
            return patterns
        else:
            if sum_if_added <= self.sum:
                patterns += self._dfs(index=index + 1, sum=sum_if_added, picked=picked_if_added)
            patterns += self._dfs(index=index + 1, sum=sum_if_not_added, picked=picked_if_not_added)
            return patterns

    def calc_patterns(self):
        if self.length > 0:
            dfs = self._dfs(index=0, sum=0, picked=0)
        else:
            dfs = 0
        patterns_by_dfs = (self.pre_patterns + 1) * dfs
        return self.pre_patterns + patterns_by_dfs


def main(n, a, x):
    dfs = DFS(average=a, numbers=x)
    result = dfs.calc_patterns()
    return result


if __name__ == '__main__':
    N, A = map(int, input().split())
    X = list(map(int, input().split()))
    print(main(N, A, X))

Fixed submission:
import numpy as np


def main(n, a, x):
    SUM_MAX = max(a, max(x)) * n + 1
    dp = np.zeros(shape=(n + 1, n + 1, SUM_MAX), dtype=int)

    dp[0][0][0] = 1
    for j in range(1, n + 1):
        for k in range(j + 1):
            dp[j][k][0:x[j - 1]] = dp[j - 1][k][0:x[j - 1]]
            if k >= 1:
                dp[j][k][x[j - 1]:] = dp[j - 1][k][x[j - 1]:] + dp[j - 1][k - 1][:SUM_MAX - x[j - 1]]

    patterns = 0
    for k in range(1, n + 1):
        ka = k * a
        patterns += dp[n][k][ka]
    return patterns


if __name__ == '__main__':
    N, A = map(int, input().split())
    X = list(map(int, input().split()))
    print(main(N, A, X))