I I U P C 2 0 0 6

Problem D: Divisibility Testing

Input: standard input
Output: standard output

 

You will be given a list of n integers, <a1 a2 a3 . . . an> and an integer k. Find out the number of ways of choosing 2 integers (ai, aj), such that ai ≤ aj and 1 ≤ i, j ≤ n and i ≠ j and (ai + aj) is divisible by k. Every pair must be distinct. Two pairs, (a, b) and (c, d), are equal if a is equal to c and b is equal to d.

 

Suppose we are given 5 integers <4 1 2 2 3> and k = 1. There are 7 ways of choosing different pairs that meets the above restrictions.

(1, 2) (1, 3) (1, 4) (2, 2) (2, 3) (2, 4) (3, 4).

 

Input

The first line of input contains an integer T that determines the number of test cases. Each test case contains two lines. The first line consists of two integers n and k. The next line contains n integers. The i-th integer gives the value of ai.

 

Output

For each test case, output the case number followed by the number of ways to choose the pairs.

 

Constraints

-           T < 100
-           1 < n < 100001
-           0 < k < 501
-           |ai| < 10000001 for any i

 

Sample Input

Output for Sample Input

2
5 1
4 1 2 2 3
5 2
4 1 2 2 3

Case 1: 7
Case 2: 3

 

Problemsetter: Sohel Hafiz