Given an array of integers and a positive integer $\boldsymbol{\mbox{k}}$, determine the number of $(i,j)$ pairs where $i<j$ and $ar[i]$ + $ar[j]$ is divisible by $\boldsymbol{\mbox{k}}$.

Example

$ar=[1,2,3,4,5,6]$

$k=5$

Three pairs meet the criteria: $[1,4],[2,3],$ and $[4,6]$.

Function Description

Complete the divisibleSumPairs function in the editor below.

divisibleSumPairs has the following parameter(s):

int n: the length of array $\boldsymbol{ar}$
int ar[n]: an array of integers
int k: the integer divisor

Returns

• int: the number of pairs

Input Format

The first line contains $2$ space-separated integers, $n$ and $\boldsymbol{\mbox{k}}$.

The second line contains $n$ space-separated integers, each a value of $arr\left[i\right]$.

Constraints

$2\leq n\leq100$
$1\leq k\leq100$
$1\leq ar[i]\leq100$

Sample Input
STDIN Function
----- --------
6 3 n = 6, k = 3
1 3 2 6 1 2 ar = [1, 3, 2, 6, 1, 2]

Sample Output
5

Explanation

Here are the $5$ valid pairs when $k=3$:

$(0,2)\rightarrow ar[0]+ar[2]=1+2=3$
$(0,5)\rightarrow ar[0]+ar[5]=1+2=3$
$(1,3)\rightarrow ar[1]+ar[3]=3+6=9$
$(2,4)\rightarrow ar[2]+ar[4]=2+1=3$
$(4,5)\rightarrow ar[4]+ar[5]=1+2=3$

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