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~ .

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.

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