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 REP(i,n)for(int i=0;i<n;i++)
#define FORD(i,a,b) for(int i=a;i>=(b);i--)
#define MP make_pair
#define F first
#define S second
typedef long long ll;
using namespace std;
int main(){
//入力の高速化用のコード
    ll n,k,s,t;cin >> n >> k >> s >> t;
    vector<ll> b(n);REP(i,n)cin >> b[i];
    vector<ll> a;
    REP(i,n){
        bool f=true;
        REP(j,18){
            if((s>>j)&1 and !((b[i]>>j)&1)){
                f=false;break;
            }
            if(!((t>>j)&1) and (b[i]>>j)&1){
                f=false;break;
            }
        }
        if(f)a.push_back(b[i]);
    }
    n=a.size();
    k=min(n,k);
    vector<map<pair<ll,ll>,ll>> dp(k);
    REP(i,n){
        FORD(j,k-2,0){
            for(auto l=dp[j].begin();l!=dp[j].end();l++){
                dp[j+1][MP((l->F.F)&a[i],(l->F.S)|a[i])]+=(l->S);
            }
        }
        dp[0][MP(a[i],a[i])]=1;
    }
    ll ans=0;
    REP(i,k)ans+=(dp[i][MP(s,t)]);
    cout << ans << endl;
}