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;
#define ll long long

const int N = 55, M = 18;
int n, k, s, t, a[N], f[1<<M];
ll ans, g[N], C[N][N];
int main() {
	scanf("%d%d%d%d", &n, &k, &s, &t);
	for(int i=0; i<n; ++i){
		scanf("%d", a+i);
		if((a[i]&s)!=s || (a[i]&t)!=a[i]) --i, --n;
		else a[i]^=s;
	}
	C[0][0]=1;
	for(int i=1; i<=n; ++i) for(int j=0; j<=i; ++j) C[i][j]=C[i-1][j]+(j?C[i-1][j-1]:0);
	for(int i=1; i<=n; ++i) for(int j=1; j<=k; ++j) g[i]+=C[i][j];
	for(int i=s^=t;; i=(i-1)&s){
		ll sum=0;
		for(int j=0; j<n; ++j) ++f[a[j]&i];
		for(int j=0; j<n; ++j) sum+=g[f[a[j]&i]], f[a[j]&i]=0;
		ans+=(__builtin_popcount(i)&1?-1:1)*sum;
		if(!i) break;
	}
	printf("%lld\n", ans);
	return 0;
}