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 Perl (v5.18.2) (judge verdict: Wrong Answer)

($H,$W,$d)=glob<>;
if($d%2){
	for(1..$W/2){
		print'RG'x($W/2),'R'x($W%2),$/;
		print'GR'x($W/2),'G'x($W%2),$/;
	}
	for(1..$W%2){
		print'RG'x($W/2),'R'x($W%2),$/;
	}
}else{
	$x=$d;
	for(0..$H-1){
		if($f==0){
			print substr+('Y'x(($d-$x)/2).'R'x$x.'B'x($d-$x).'G'x$x.'Y'x(($d-$x)/2))x($W/$d+1),0,$W;
			print$/;
			$x-=2;
			if($x==0){++$f}
		}elsif($f==1){
			print substr+('Y'x(($d-$x)/2).'G'x$x.'B'x($d-$x).'R'x$x.'Y'x(($d-$x)/2))x($W/$d+1),0,$W;
			print$/;
			$x+=2;
			if($x==$d){++$f}
		}elsif($f==2){
			print substr+('B'x(($d-$x)/2).'G'x$x.'Y'x($d-$x).'R'x$x.'B'x(($d-$x)/2))x($W/$d+1),0,$W;
			print$/;
			$x-=2;
			if($x==0){++$f}
		}elsif($f==3){
			print substr+('B'x(($d-$x)/2).'R'x$x.'Y'x($d-$x).'G'x$x.'B'x(($d-$x)/2))x($W/$d+1),0,$W;
			print$/;
			$x+=2;
			if($x==$d){$f=0}
		}
	}
}