You are given an array, find the minimum k, such that the count of number of subarrays whose xor is atmost k, is atleast x.

1<=N<=1e5

1<=X<=N*(N+1)/2

Sample Input

4 7

1 2 3 4

Output

4

Subarrays are

{1} {1,2} {1,2,3} {2,3} {2} {3} {4} {1,2,3,4} (count of number of subarrays with xor atmost 4 is 8)

Note: XOR of a subarray is the xor of all the elements in the subarray

I tried binary searching on k, and each time found the count of subarrays with xor less or

equal to k, but that involved trie and heavy implementation, any other simpler approach?