Problem Statement

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.

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.

Constraints

• $1 \leq N \leq 50$
• $1 \leq K \leq N$
• $0 \leq A_i < 2^{18}$
• $0 \leq S < 2^{18}$
• $0 \leq T < 2^{18}$
• $A_i \neq A_j (1 \leq i < j \leq N)$

Sample Input 1

3 3 0 3
1 2 3

Sample Output 1

2

The conditions are satisfied when we choose {1,2} or {1,2,3}.

Sample Input 2

5 3 1 7
3 4 9 1 5

Sample Output 2

2

Sample Input 3

5 4 0 15
3 4 9 1 5

Sample Output 3

3

见题面 Input 部分

见题面 Output 部分