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;
typedef long long int ll;
typedef pair<ll,ll> mp;
ll inf =  1e9;


int main(){
 ll n,k,s,t;
 cin>>n>>k>>s>>t;
 vector<ll> a(n);
 for(ll i=0;i<n;i++)cin>>a[i];
 //map<mp,ll> cnt;//積，和
 vector< map<mp,ll> > cnt(k+1);
 //cnt[0][ mp((1ll<<19)-1, 0 ) ] = 1;
 for(ll i=0;i<n;i++){
  //map<mp,ll> tmp = cnt;
  for(ll j=k;j>=2;j--){
   for(auto it:cnt[j-1]){
    cnt[j][ mp( it.first.first & a[i] , it.first.second | a[i] ) ] += it.second;
   }
  }
  //cnt = tmp;
  cnt[1][ mp( a[i] , a[i] ) ]++;
  //cout<<"i: "<<i<<endl;
  //for(auto it:cnt) cout<<it.first.first<<' '<<it.first.second<<' '<<it.second<<endl;
 }
 //for(auto i:cnt)cout<<i.first.first<<' '<<i.first.second<<' '<<i.second<<endl;
 //cout<<cnt[mp(s,t)]<<endl;
 ll sum = 0;
 for(ll i=0;i<=k;i++)sum+=cnt[i][mp(s,t)];
 cout<<sum<<endl;
 return 0;
}