Problem:
Score : 700 points

Problem Statement

We have a grid with H rows and W columns of squares.
We will represent the square at the i-th row from the top and j-th column from the left as (i,\ j).
Also, we will define the distance between the squares (i_1,\ j_1) and (i_2,\ j_2) as |i_1 - i_2| + |j_1 - j_2|.

Snuke is painting each square in red, yellow, green or blue.
Here, for a given positive integer d, he wants to satisfy the following condition:

No two squares with distance exactly d have the same color.

Find a way to paint the squares satisfying the condition.
It can be shown that a solution always exists.

Constraints

2 ≤ H, W ≤ 500

1 ≤ d ≤ H + W - 2

Input

Input is given from Standard Input in the following format:

H W d

Output

Print a way to paint the squares satisfying the condition, in the following format. If the square (i,\ j) is painted in red, yellow, green or blue, c_{ij} should be R, Y, G or B, respectively.

c_{11}c_{12}...c_{1W}
:
c_{H1}c_{H2}...c_{HW}

Sample Input 1

2 2 1

Sample Output 1

RY
GR

There are four pairs of squares with distance exactly 1.
As shown below, no two such squares have the same color.

(1,\ 1), (1,\ 2) : R, Y

(1,\ 2), (2,\ 2) : Y, R

(2,\ 2), (2,\ 1) : R, G

(2,\ 1), (1,\ 1) : G, R

Sample Input 2

2 3 2

Sample Output 2

RYB
RGB

There are six pairs of squares with distance exactly 2.
As shown below, no two such squares have the same color.

(1,\ 1) , (1,\ 3) : R , B

(1,\ 3) , (2,\ 2) : B , G

(2,\ 2) , (1,\ 1) : G , R

(2,\ 1) , (2,\ 3) : R , B

(2,\ 3) , (1,\ 2) : B , Y

(1,\ 2) , (2,\ 1) : Y , R

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.Scanner;

/**
 * Created by torum on 2017/09/23.
 */
public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int H= sc.nextInt();
        int W= sc.nextInt();
        int d= sc.nextInt();
        int[][] colors = new int[H][W];

        for(int i = 0;i < H;i++){
            for(int j = 0;j < W;j++){
                colors[i][j] = 0;
            }
        }
        colors[0][0] = 0;
        for(int i = 0;i < H;i++){
            for(int j = 0;j < W;j++){
                int nowcolor = colors[i][j];
                for(int s = 0;s< d;s++){
                    if(i+s < H && j+(d-s) < W){
                        if(colors[i+s][j+(d-s)]%4 == nowcolor%4){
                            colors[i+s][j+(d-s)] = nowcolor+1;
                        }
                    }
                    if(i-s >= 0 && j+(d-s) < W){
                        if( colors[i-s][j+(d-s)]%4 == nowcolor%4){

                            colors[i-s][j+(d-s)] = nowcolor+1;
                        }
                    }
                    if(i+s < H && j-(d-s) >= 0){
                        if(colors[i+s][j-(d-s)]%4 == nowcolor%4){

                            colors[i+s][j-(d-s)] = nowcolor+1;
                        }
                    }
                    if(i-s >= 0 && j-(d-s) >= 0){
                        if( colors[i-s][j-(d-s)]%4 == nowcolor%4){
                            colors[i-s][j-(d-s)] = nowcolor+1;
                        }
                    }
                }
            }
        }
        for(int i = 0;i < H;i++){
            for(int j = 0;j < W;j++){
             switch(colors[i][j]%4){
                 case 0:
                     System.out.print("R");
                     break;
                 case 1:
                     System.out.print("Y");
                     break;
                 case 2:
                     System.out.print("G");
                     break;
                 case 3:
                     System.out.print("B");
                     break;
             }
            }
            System.out.println();
        }


    }
}