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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
import math
import copy
from heapq import heappush, heappop, heapify
from functools import cmp_to_key
from bisect import bisect_left, bisect_right
from collections import defaultdict, deque, Counter
sys.setrecursionlimit(1000000)

# input aliases
input = sys.stdin.readline
getS = lambda: input().strip()
getN = lambda: int(input())
getList = lambda: list(map(int, input().split()))
getZList = lambda: [int(x) - 1 for x in input().split()]

INF = float("inf")
MOD = 10**9 + 7
divide = lambda x: pow(x, MOD-2, MOD)

def search(arr):
    ret = [0] * 3000
    ret[0] = 1
    for num in arr:
        tmp = copy.copy(ret)
        for i in range(2700):
            tmp[i + num] += ret[i]
        ret = tmp
    return ret

def solve():
    n, k = getList()
    nums = getList()
    pos = []
    neg = []
    zero = 0
    for num in nums:
        if num == k:
            zero += 1
        if num < k:
            neg.append(k - num)
        if num > k:
            pos.append(num - k)

    posarr = search(pos)
    negarr = search(neg)

    ans = 0
    for i in range(2800):
        ans += posarr[i] * negarr[i]
    # print(posarr)
    # print(negarr)
    print(ans * pow(2, zero) - 1)

def main():
    n = getN()
    for _ in range(n):
        solve()

    return
if __name__ == "__main__":
    # main()
    solve()