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;

const int maxN = 55;
const int maxB = 18;
typedef long long ll;

int A[maxN], vis[maxN], as[maxB];
ll C[maxN][maxN], ans;
map<int, int> M;

void init(){
	int i, j;
	for(i = 0; i < maxN; ++i){
		C[i][0] = C[i][i] = 1;
		for(j = 1; j < i; ++j)
			C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
	}
	for(i = 0; i < maxN; ++i){
		for(j = 2; j < maxN; ++j)
			C[i][j] += C[i][j - 1];
	}
}

int main (){
	int n, k, S, T, i, j, c = 0, b;
	scanf("%d%d%d%d", &n, &k, &S, &T);
	for(init(), i = 0; i < n; ++i) scanf("%d", A + i);
	for(i = 0; i < maxB; ++i){
		b = 1 << i;
		if(S & b){
			if(T & b) { for(j = 0; j < n; ++j) if(!(A[j] & b)) vis[j] = 1; }
			else { puts("0"); return 0; }
		}
		else{
			if(T & b) as[c++] = i;
			else { for(j = 0; j < n; ++j) if(A[j] & b) vis[j] = 1; }
		}
	}
	for(i = j = 0; i < n; ++i) if(!vis[i]) A[j++] = A[i]; n = j;
	for(b = 0; b < (1 << c); ++b){
		int sgn = 1, s = 0;
		for(i = 0; i < c; ++i) if(b & (1 << i)) s |= (1 << as[i]), sgn *= -1;
		for(M.clear(), i = 0; i < n; ++i) ++M[A[i] & s];
		for(auto it : M) ans += sgn * C[it.second][k];
	}
	printf("%lld\n", ans);
	return 0;
}