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 Rust (1.15.1) (judge verdict: Accepted)

use std::io;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

fn lms(a: usize, b: usize) -> usize {
    let mut x = cmp::max(a,b);
    let mut y = cmp::min(a,b);
    while x%y > 0 {
        let z = x % y;
        x = y;
        y = z;
    }
    y
}

fn main() {
    let nk: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let n = nk[0];
    let k = nk[1];

    if k % 2 == 0 {
        let div = (n / k) as u64;
        let div2 = ((n+k/2) / k) as u64;
        println!("{}", div * div * div + div2 * div2 * div2);
    } else {
        let div = (n / k) as u64;
        println!("{}", div * div * div);
    }
}