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 static java.lang.System.out;
import java.io.InputStream;
import java.io.IOException;
import java.util.NoSuchElementException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;

public class Main {
    public static void main(String args[]) {
        MyInput in = new MyInput();
        int H = in.nextInt();
        int W = in.nextInt();
        int d = in.nextInt();
        String[][] map = new String[H][W];

        String[] clr = {"R","Y","G","B"};
        boolean[][][] used = new boolean[4][H][W];
        int tmp = 0;
        for(int i = 0; i < H; i++) {
            for(int k = 0; k < W; k++) {
                for(int l = 0 ; l < 4; l++) {
                    if(!used[l][i][k]) {
                        map[i][k] = clr[l];
                        tmp = l;
                    }
                }
                for(int l = 0 ; l <= d; l++) {
                    if(i+l < H && k+d-l < W) {
                        used[tmp][i+l][k+(d-l)] = true;
                    }
                    if(i+l < H && k-(d-l) >= 0) {
                        used[tmp][i+l][k-(d-l)] = true;
                    }
                }
            }
        }
        for(int i = 0; i < H; i++) {
            for(int k = 0; k < W; k++) {
                out.print(map[i][k]);
            }
            out.println();
        }

    }
}

class MyInput {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr= 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if(ptr < buflen) {
			return true;
		}else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch(IOException e) {
				e.printStackTrace();
			}
			if(buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	public int readByte() { 
		if (hasNextByte()) return buffer[ptr++];
		else return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <=126;
	}

	private void skipUnprintable() {
		while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
	}

	public boolean hasNext() {
		skipUnprintable();
		return hasNextByte();
	}

	public String next() {
		if(!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if(!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if(b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true) {
			if('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			}else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		long nl = nextLong();
		if(nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}