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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		
		int N = in.nextInt();
		int Q = in.nextInt();
		
		
		
		System.out.println(count(N, Q));
		//System.out.println(count_tu(N, Q));
		
		

	}
	
	public static long count(int N, int Q) {
		
		long ans=0;
		long t;
		if (Q%2==0) {
			int P = Q/2;
			t=N/P;
			if (t%2==0) {
				ans=(t/2)*(t/2)*(t/2)*2;
			}else {
				ans=(t/2)*(t/2)*(t/2) + ((t/2)+1)*((t/2)+1)*((t/2)+1);
			}
			
		} else {
			t=N/Q;
			ans = t*t*t;
			
		}
		
		return ans;
	}
	
	public static long count_tu(int N, int Q) {
		
		long ans = 0;
		
		if (Q%2==0) {
			int P = Q/2;
			for (int i=P;i<=N;i+=P) {
				for (int j=P;j<=N;j+=P) {
					if ((i+j)%Q != 0)
						continue;
					else {				
						for (int k=P;k<=N;k+=P) {
							
							if ((k+j)%Q != 0||(k+i)%Q != 0)
								continue;
							else {
							
								ans++;
								System.out.println(i + " " + j + " " + k);
							
							}
						}
					}
				}
			}
		} else {
			for (int i=Q;i<=N;i+=Q) {
				for (int j=Q;j<=N;j+=Q) {
					if ((i+j)%Q != 0)
						continue;
					else {				
						for (int k=Q;k<=N;k+=Q) {
							
							if ((k+j)%Q != 0||(k+i)%Q != 0)
								continue;
							else {
							
								ans++;
								System.out.println(i + " " + j + " " + k);
							
							}
						}
					}
				}
			}
			
		}
		return ans;
	}

}