10500: ABC108 —— C - Triangular Relationship
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Description
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.
Input
Input is given from Standard Input in the following format:
```
$N$ $K$
```
```
$N$ $K$
```
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 $K$.
Constraints
- $1 \leq N,K \leq 2\times 10^5$
- $N$ and $K$ are integers.
- $N$ and $K$ are integers.
Sample 1 Input
3 2
Sample 1 Output
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 2 Input
5 3
Sample 2 Output
1
Sample 3 Input
31415 9265
Sample 3 Output
27
35897 932
114191