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