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:
#import<bits/stdc++.h>
using namespace std;
int N,K,S,T,U,i,j;
vector<int>A;
long c[51][51]={1},P[51],a,w;
int main()
{
	for(cin>>N>>K>>S>>T;cin>>j;){if(!(~j&S|j&~T))A.push_back(j);for(c[++i][j=0]=1;j++<K;)P[i]+=c[i][j]=c[i-1][j-1]+c[i-1][j];}
	for(;U<1<<18;w=!++U)
	{
		map<int,int>M;
		for(int v:A)M[v&U]++;
		for(auto[p,q]:M)w+=P[q];
		if(!(~U&S|U&~T))a+=__builtin_parity(U&~S)?-w:w;
	}
	cout<<a;
}