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: Time Limit Exceeded)


fn func(input_str: &str) {
    let mut iter = input_str.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let k: usize = iter.next().unwrap().parse().unwrap();
    let mut ans = 0;
    for z in 1..(2 * n / k + 2) {
        for y in 1..(z + 1) {
            for x in 1..(y + 1) {
                if x + y <= z {
                    continue;
                }
                let da = (y + z - x) * k;
                let db = (x + y - z) * k;
                let dc = (x + z - y) * k;
                if da > 2 * n || db > 2 * n || dc > 2 * n
                    || da % 2 + db % 2 + dc % 2 > 0 {
                     continue;
                }
                if da == db && db == dc && da == dc {
                    ans += 1;
                } else if da != db && db != dc && dc != da {
                    ans += 6;
                } else {
                    ans += 3;
                }
            }
        }
    }
    println!("{}", ans);
}

use std::io::Read;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    func(&buf[..]);
}