Problem: 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}

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}

Examples

Input

2 2 1


Output

RY
GR


Input

2 3 2


Output

RYB
RGB

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	static PrintWriter out;
	static InputReader ir;
	static boolean debug = false;

	static void solve() {
		int h = ir.nextInt();
		int w = ir.nextInt();
		int d = ir.nextInt();
		char[][] map = new char[h][w];
		if (d % 2 == 1) {
			for (int i = 0; i < h; i++)
				for (int j = 0; j < w; j++)
					map[i][j] = ((i + j) % 4 == 0 ? 'R' : ((i + j) % 4 == 1) ? 'Y' : ((i + j) % 4 == 2) ? 'G' : 'B');
		} else {
			for (int i = 0; i < h; i++)
				for (int j = 0; j < w; j++) {
					if ((i + j) % (2 * d) < d) {
						int k = (i + j) % (2 * d);
						if (i < k / 2)
							map[i][j] = 'Y';
						else {
							if ((i - k / 2) % d < d / 2)
								map[i][j] = 'R';
							else
								map[i][j] = 'Y';
						}
					} else {
						int k = (i + j) % (2 * d) - d;
						if (i < k / 2)
							map[i][j] = 'B';
						else {
							if ((i - k / 2) % d < d / 2)
								map[i][j] = 'G';
							else
								map[i][j] = 'B';
						}
					}
				}
		}
		for (int i = 0; i < h; i++)
			out.println(map[i]);
	}

	public static void main(String[] args) {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

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

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

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

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

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

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

		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public long[] nextLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}

	static void tr(Object... o) {
		if (debug)
			out.println(Arrays.deepToString(o));
	}
}