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>
using namespace std;
using ll=long long;

int N,K,A[50],S,T;
ll res;
map<pair<int,pair<int,int>>,ll>mp;

int main(){
	cin>>N>>K>>S>>T;
	for(int i=0;i<N;i++){
		cin>>A[i];
	}
	for(int i=0;i<N;i++){
		if((A[i]&S)==S&&(A[i]|T)==T){
			queue<pair<pair<int,pair<int,int>>,ll>>q;
			for(auto p:mp){
				if(p.first.first==K)continue;
				q.push({{p.first.first+1,{p.first.second.first&A[i],p.first.second.second|A[i]}},p.second});
			}
			while(!q.empty()){
				mp[q.front().first]+=q.front().second;
				q.pop();
			}
			mp[{1,{A[i],A[i]}}]++;
		}
	}
	for(int i=1;i<=K;i++)res+=mp[{i,{S,T}}];
	cout<<res<<endl;
}