One day, ZS the Coder wrote down an array of integers a with elements a₁,  a₂,  ...,  a_n.

A subarray of the array a is a sequence a_l,  a_{l  +  1},  ...,  a_r for some integers (l,  r) such that 1  ≤  l  ≤  r  ≤  n. ZS the Coder thinks that a subarray of a is beautiful if the bitwise xor of all the elements in the subarray is at least k.

Help ZS the Coder find the number of beautiful subarrays of a!

The first line contains two integers n and k (1 ≤ n ≤ 10⁶, 1 ≤ k ≤ 10⁹) — the number of elements in the array a and the value of the parameter k.

The second line contains n integers a_i (0 ≤ a_i ≤ 10⁹) — the elements of the array a.

Print the only integer c — the number of beautiful subarrays of the array a.