You are given an array of integers A = (a0, a1, ..., an-1) and a positive integer k. Find and print the number of pairs (i, j) where i < j and ai + aj is divisible by k.

Input

The first line contains integer n (2 ≤ n, k ≤ 100) and k. The second line contains n space-separated integers describing the values of A = (a0, a1, ..., an-1) (1 ≤ ai ≤ 100).

Output

Print the number of pairs (i, j) where i < j and ai + aj is divisible by k.