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 $a_{i} \oplus a_{j} = x$, where $\oplus$ is bitwise xor operation (see notes for explanation).

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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 ≤ 10^5, 0 ≤ x ≤ 10^5) — the number of elements in the array and the integer x.

Second line contains n integers a_1, a_2, ..., a_{n} (1 ≤ a_{i} ≤ 10^5) — the elements of the array.

-----Output-----

Print a single integer: the answer to the problem.

-----Examples-----

Input 2 3 1 2

Output 1 Input 6 1 5 1 2 3 4 1

Output 2

-----Note-----

In the first sample there is only one pair of i = 1 and j = 2. $a_{1} \oplus a_{2} = 3 = x$ so the answer is 1.

In the second sample the only two pairs are i = 3, j = 4 (since $2 \oplus 3 = 1$) and i = 1, j = 5 (since $5 \oplus 4 = 1$).

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.