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

#include<bits/stdc++.h>
#define REP(n)for(ll i=0;i<n;i++)
#define M make_pair
#define F first
typedef long long ll;
using namespace std;
int main(){
    ll n,k,s,t,a[50];cin>>n>>k>>s>>t;
    REP(n)cin>>a[i];
    map<pair<ll,ll>,ll> p[50];
    REP(n){
        for(ll j=k-2;j+1;j--){
            for(const auto&l:p[j]){
                p[j+1][M(l.F.F&a[i],l.F.second|a[i])]+=l.second;
            }
        }
        p[0][M(a[i],a[i])]=1;
    }
    n=0;
    REP(k)n+=p[i][M(s,t)];
    cout<<n;
}