Super Array

Robin found an array A of size N which he wants to convert into super array.

To do this he decided to choose first or last element do one of the following operation with equal probability B times.

After performing all operations, if the array consist of atleast C elements greater than the special value of array then the array is called super array.

Special value is the bitwise XOR of all elements.

Find and return the total number of possible super array, he can get by performing the above operations.

1 <= N <= 10

1 <= A[i] <= 10⁹

1 <= B, C <= N

First argument is an integer array A of size N.

Second argument is an integer B.

Third argument is an integer C.

Return an integer denoting the possible number of super array.

Input 1:

 A = [10, 2, 10, 5]
 B = 3
 C = 3

Input 2:

 A = [3, 3, 4]
 B = 3
 C = 2

Output 1:

 1

Output 2:

 3

Explanation 1:

 Special value will be 7.
 There will be only one possible super array: [10, 2, 10, 8]. 
 Perform three operation by incrementing last element.

Explanation 2:

 There will be 3 possible super array.