Problem:
Score : 800 points

Problem Statement

Given are N pairwise distinct non-negative integers A_1,A_2,\ldots,A_N.
Find the number of ways to choose a set of between 1 and K numbers (inclusive) from the given numbers so that the following two conditions are satisfied:

The bitwise AND of the chosen numbers is S.

The bitwise OR of the chosen numbers is T.

Constraints

1 \leq N \leq 50

1 \leq K \leq N

0 \leq A_i < 2^{18}

0 \leq S < 2^{18}

0 \leq T < 2^{18}

A_i \neq A_j (1 \leq i < j \leq N)

Input

Input is given from Standard Input in the following format:

N K S T
A_1 A_2 ... A_N

Output

Print the answer.

Sample Input 1

3 3 0 3
1 2 3

Sample Output 1

2

The conditions are satisfied when we choose \{1,2\} or \{1,2,3\}.

Sample Input 2

5 3 1 7
3 4 9 1 5

Sample Output 2

2

Sample Input 3

5 4 0 15
3 4 9 1 5

Sample Output 3

3

Solution in Python (3.8.2) (judge verdict: Time Limit Exceeded)

import math
import itertools


def main():
    n, k, s, t = list(map(int, input().split()))
    a = list(map(int, input().split()))

    # mask = 1 << (math.ceil(math.sqrt(s)) + 1) - 1
    a.sort()
    for i, e in enumerate(a):
        if s <= e:
            break
    else:
        return 0

    max_value = 2 ** math.ceil(math.sqrt(t))
    for j, e in enumerate(a):
        if max_value < e:
            break

    result = 0
    cand = []
    for m in range(i, j + 1):
        if (s & a[m]) == s and (t | a[m]) == t:
            cand.append(a[m])
            if a[m] == s and a[m] == t:
                result += 1

    for i in range(2, k + 1):
        for c in itertools.combinations(cand, i):
            sr = c[0]
            tr = 0

            for e in c:
                sr &= e
                tr |= e
            if sr == s and tr == t:
                result += 1

    return result

if __name__ == '__main__':
    result = main()
    print(result)