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 <iostream>
#include <vector>
#include <map>
#include <utility>
using namespace std;

int main()
{
    int N, K, S, T;
    cin>>N>>K>>S>>T;
    vector<int> A(N);
    for (int &a: A)
        cin>>a;

    vector<map<pair<int, int>, long long>> X(K+1);
    X[0][make_pair(0x3ffff, 0)] = 1;
    for (int &a: A)
    {
        if ((a&S)==S && (a|T)==T)
            for (int k=K-1; k>=0; k--)
                for (auto x: X[k])
                    X[k+1][make_pair(x.first.first&a, x.first.second|a)] += x.second;
    }
    long long ans = 0;
    for (int k=1; k<=K; k++)
        ans += X[k][make_pair(S, T)];
    cout<<ans<<endl;
}