C - Triangular Relationship

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 $K$.

3 2

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.

5 3

1

31415 9265

27

35897 932

114191