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 Python (3.4.3) (judge verdict: Runtime Error)

import sys

H, W, d = map(int, input().split())

color = 'RGBY'
ret = [['' for _ in range(W)] for _ in range(H)]
flag = [[0b1111 for _ in range(W)] for _ in range(H)]

for i in range(H):
    for j in range(W):
        for k in range(4):
            if flag[i][j] & 2 ** k:
                flag[i][j] &= ~(2 ** k)
                ret[i][j] = color[k]

                for p in range(d + 1):
                    q = d - p

                    if p >= i and q >= j: flag[i - p][j - q] &= ~(2 ** k)
                    if p < H - i and q >= j: flag[i + p][j - q] &= ~(2 ** k)
                    if p >= i and q < W - j: flag[i - p][j + q] &= ~(2 ** k)
                    if p < H - i and q < W - j: flag[i + p][j + q] &= ~(2 ** k)
                break

        # なにも入らなかった
        if ret[i][j] is '':
            print('hoge')

for a in ret:
    print(''.join(a))