M-arrays

1000ms

262144K

Description:

You are given an array $$$a_1, a_2, \ldots, a_n$$$ consisting of $$$n$$$ positive integers and a positive integer $$$m$$$.

You should divide elements of this array into some arrays. You can order the elements in the new arrays as you want.

Let's call an array $$$m$$$-divisible if for each two adjacent numbers in the array (two numbers on the positions $$$i$$$ and $$$i+1$$$ are called adjacent for each $$$i$$$) their sum is divisible by $$$m$$$. An array of one element is $$$m$$$-divisible.

Find the smallest number of $$$m$$$-divisible arrays that $$$a_1, a_2, \ldots, a_n$$$ is possible to divide into.

Input:

The first line contains a single integer $$$t$$$ $$$(1 \le t \le 1000)$$$ — the number of test cases.

The first line of each test case contains two integers $$$n$$$, $$$m$$$ $$$(1 \le n \le 10^5, 1 \le m \le 10^5)$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ $$$(1 \le a_i \le 10^9)$$$.

It is guaranteed that the sum of $$$n$$$ and the sum of $$$m$$$ over all test cases do not exceed $$$10^5$$$.

Output:

For each test case print the answer to the problem.

Sample Input:

4
6 4
2 2 8 6 9 4
10 8
1 1 1 5 2 4 4 8 6 7
1 1
666
2 2
2 4

Sample Output:

Note:

In the first test case we can divide the elements as follows:

$$$[4, 8]$$$. It is a $$$4$$$-divisible array because $$$4+8$$$ is divisible by $$$4$$$.
$$$[2, 6, 2]$$$. It is a $$$4$$$-divisible array because $$$2+6$$$ and $$$6+2$$$ are divisible by $$$4$$$.
$$$[9]$$$. It is a $$$4$$$-divisible array because it consists of one element.

Informação

Provedor Codeforces

Código CF1497B