B. Arpa’s obvious problem and Mehrdad’s terrible solution(Hard)
time limit per test
0.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

There are some beautiful girls in Arpa’s land as mentioned before.

Once Arpa came up with an obvious problem:

Given an array and a number x, count the number of pairs of indices i, j (1 ≤ i < j ≤ n) such that , where is bitwise xor operation.

Immediately, Mehrdad discovered a terrible solution that nobody trusted. Now Arpa needs your help to implement the solution to that problem.

Input

First line contains two integers n and x (1 ≤ n ≤ 2·106, 0 ≤ x ≤ 2107) — the number of elements in the array and the integer x.

Second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 2107) — the elements of the array. It's guaranteed that .

Input compression : x and ais are given in 32 base numerical system (i.e. "V"  = 31, "H9"  = 17·32 + 9 = 480).

It's guaranteed that no number starts with zero in the input.

Output

Print a single integer: the answer to the problem.

Examples
Input
2 3
1 2
Output
1
Input
4 1
A C E F
Output
1
Note

A bitwise xor takes two bit integers of equal length and performs the logical xor operation on each pair of corresponding bits. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1. You can read more about bitwise xor operation here: https://en.wikipedia.org/wiki/Bitwise_operation#XOR.