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: Runtime Error)

import java.io.FileInputStream;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class Main{
	static Scanner sc;

	static int H, W, d;

	public static void main(String[] args) throws Exception {
		//InputStream in = new FileInputStream("src/input.txt");
		InputStream in = System.in;
		//PrintStream out = new PrintStream("src/output.txt");

		//System.setOut(out);

		sc = new Scanner(in);

		H = sc.nextInt();
		W = sc.nextInt();
		d = sc.nextInt();

	//	HashSet<String> map = new HashSet<String>();
		ArrayList<ArrayList<HashSet<String>>> map = new ArrayList<ArrayList<HashSet<String>>>();

		for(int i = 0; i < H; i++){
			map.add(new ArrayList<HashSet<String>>());
			for(int j = 0; j < W; j++){
				map.get(i).add(new HashSet<String>());
				map.get(i).get(j).add("R");
				map.get(i).get(j).add("Y");
				map.get(i).get(j).add("G");
				map.get(i).get(j).add("B");
			}
		}

		run(map, 0);
	}

	static void run(ArrayList<ArrayList<HashSet<String>>> map, int num){
		int h = (int)(num / W);
		int w = num % W;
		if(h == H){
			//System.out.println("OK");
			for(int i = 0; i < H; i++){
				for(int j = 0; j < W; j++){
					System.out.print(map.get(i).get(j).iterator().next());
				}
				System.out.println();
			}
			System.exit(1);
			return;
		}

		ArrayList<ArrayList<HashSet<String>>> newMap = new ArrayList<ArrayList<HashSet<String>>>();
		for(int i = 0; i < H; i++){
			newMap.add(new ArrayList<HashSet<String>>());
			for(int j = 0; j < W; j++){
				newMap.get(i).add(new HashSet<String>());
				newMap.get(i).get(j).addAll(map.get(i).get(j));
			}
		}
		for (String color : map.get(h).get(w)) {
			newMap.get(h).get(w).clear();
			newMap.get(h).get(w).add(color);
			for(int i = 0; i < H; i++){
				for(int j = 0; j < W; j++){
					if(Math.abs(h - i) + Math.abs(w - j) == d){
						newMap.get(i).get(j).remove(color);
						if(newMap.get(i).get(j).size() == 0){
							return;
						}
					}
				}
			}
			run(newMap, num+1);
		}
	}
}