Problem: 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.

Examples

Input

3 3 0 3
1 2 3


Output

2


Input

5 3 1 7
3 4 9 1 5


Output

2


Input

5 4 0 15
3 4 9 1 5


Output

3

Solution (in CPP):

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