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 UL=unsigned int;
using LL=long long;
using ULL=unsigned long long;
#define rep(i,n) for(LL i=0; i<(n); i++)

LL N,K,S,T;
LL A[50];
LL pc[1<<18]={};
LL D[1<<18];
LL C[51][51];
LL X[51]={};

int main(){
 cin>>N>>K>>S>>T;
 rep(i,N) cin>>A[i];
 if(S&~T){ cout<<0<<endl; return 0; }
 rep(i,N) if((~T&A[i])|(S&~A[i])){ swap(A[i],A[N-1]); i--; N--; }
 rep(i,1<<18) if(i) pc[i]=pc[i&(i-1)]+1;
 T^=S;
 rep(n,51){ C[n][0]=C[n][n]=1; rep(r,n-1) C[n][r+1]=C[n-1][r]+C[n-1][r+1]; }
 X[0]=1; rep(n,50){ X[n+1]=X[n]*2; if(n>=K) X[n+1]-=C[n][K]; }
 for(LL n=50; n>=0; n--) X[n+1]-=X[n];
 LL ans=0;
 rep(t,T+1){
  if(t&~T) continue;
  LL tmp=0;
  rep(i,N) D[A[i]&t]=0;
  rep(i,N){ D[A[i]&t]++; tmp+=X[D[A[i]&t]]; }
  if(pc[t]&1) ans-=tmp; else ans+=tmp;
 }
 cout<<ans<<endl;
 return 0;
}