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<map>
using namespace std;
int N,K,S,T,A[50];
long c[51][51],P[51],ans,now;
int main()
{
	cin>>N>>K>>S>>T;
	for(int i=0;i<N;i++)cin>>A[i];
	c[0][0]=1;
	for(int i=0;i++<N;)
	{
		c[i][0]=1;
		for(int j=0;j++<K;)P[i]+=c[i][j]=c[i-1][j-1]+c[i-1][j];
	}
	for(int U=0;U<1<<18;U++)
	{
		map<int,int>M;
		for(int i=0;i<N;i++)~A[i]&S||A[i]&~T||M[A[i]&U]++;
		now=0;
		for(auto p:M)now+=P[p.second];
		if(!(~U&S||U&~T))ans+=__builtin_parity(U&~S)?-now:now;
	}
	cout<<ans<<endl;
}