201020: [AtCoder]ARC102 C - Triangular Relationship

Memory Limit:1024 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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

Input

题意翻译

给您整数 $N$ 和 $K$。 找出不大于 $N$ 的正整数的三元组 $(a,b,c)$ 的数量,以使 $a+b$,$b+c$ 和 $c+a$ 均为 $K$ 的倍数。 $a,b,c$ 的顺序确实很重要,其中一些可以相同。

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