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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {


    public static void main(String[] args) {
        try (CustomReader in = new CustomReader()) {
            new Main().execute(in);
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    public void execute(CustomReader in) throws IOException {
        int[] nk = in.readLineAsIntArray();
        final int N = nk[0];
        final int K = nk[1];

        long[] countByMod = new long[K];

        for (int i = 1; i <= N; i++) {
            countByMod[i % K]++;
        }

        long total = 0L;
        for (int i = 0; i < K; i++) {
            int ma = i;
            int mb = (K - ma) % K;
            int mc = (K - mb) % K;
            if ((ma + mc) % K == 0) {
                total += countByMod[ma] * countByMod[mb] * countByMod[mc];
            }
        }
        System.out.println(total);

    }


    static class CustomReader extends BufferedReader {
        public CustomReader() throws IOException {
            super(new InputStreamReader(System.in));
        }

        public int readLineAsInt() throws IOException {
            return Integer.parseInt(readLine());
        }

        public int[] readLineAsIntArray() throws IOException {
            String[] strArray = this.readLine().split(" ");
            int[] intArray = new int[strArray.length];
            for (int i = 0, n = strArray.length; i < n; i++) {
                intArray[i] = Integer.parseInt(strArray[i]);
            }
            return intArray;
        }

        public int[][] readAsIntMatrix(int rows, int columns) throws IOException {
            int[][] matrix = new int[rows][columns];
            for (int i = 0; i < rows; i++) {
                String[] r = this.readLine().split(" ");
                for (int j = 0; j < columns; j++) {
                    matrix[i][j] = Integer.parseInt(r[j]);
                }
            }
            return matrix;
        }

        public char[][] readAsCharMatrix(int rows) throws IOException {
            char[][] matrix = new char[rows][];
            for (int i = 0; i < rows; i++) {
                matrix[i] = this.readLine().toCharArray();
            }
            return matrix;
        }

    }

}