Problem:
Score : 300 points

Problem Statement

You are given integers N and K. Find the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.
The order of a,b,c does matter, and some of them can be the same.

Constraints

1 \leq N,K \leq 2\times 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.

Sample Input 1

3 2

Sample Output 1

9

(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.

Sample Input 2

5 3

Sample Output 2

1

Sample Input 3

31415 9265

Sample Output 3

27

Sample Input 4

35897 932

Sample Output 4

114191

Solution in Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (N, K) = readLine()!!.split(" ").map { it.toLong() }

    var answer = 0L
    // a + b = k
    //println(answer)
    // Fix a + b
    // a % K をM固定すると
    //  b = K - m
    // c = K- m と決まる
    val num = LongArray(K.toInt(), { 0L })
    (1..N).forEach {
        num[it.mod(K).toInt()]++
    }


    (0 until K).forEach { a ->
        // a +b = K
        val b = (K - a).mod(K)
        // a +c = K
        val c = (K - a).mod(K)
        // check b + c
        if ((b + c).mod(K) == 0L) {
            answer += num[a.toInt()] * num[b.toInt()] * num[c.toInt()]
        }
    }
    println(answer)
}