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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
 
#define ll long long
#define all(aaa) aaa.begin(), aaa.end()

const int N = 1005;
char s[N][N], t[4] = {'R', 'Y', 'G', 'B'};
int n, m, d;

bool paint(int sx, int sy, int z, char letter) {
    bool painted_cell = false;

    int k = sy, j = sx;
    for (int i = 2; i <= z; i += 2, k--, j++) {
        for (int h = 0; h < i; h++) {
            if (j >= 0 && j < n && k + h >= 0 && k + h < m) {
                s[j][k + h] = letter;
                painted_cell = true;
            }
        }
    }
    k += 2;
    for (int i = z - 2; i >= 2; i -= 2, k++, j++) {
        for (int h = 0; h < i; h++) {
            if (j >= 0 && j < n && k + h >= 0 && k + h < m) {
                s[j][k + h] = letter;
                painted_cell = true;
            }
        }
    }
    return painted_cell;
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    cin >> n >> m >> d;

    if (d % 2)
        d++;

    for (int i = -N; i < N * 2; i += d) {
        for (int j = -N; j < N * 2; j += d) {
            if (paint(i, j, d, t[(i + N + j + N) / d & 1])) {

            }
        }
    }

    for (int i = -N; i < N * 2; i += d) {
        for (int j = -N; j < N * 2; j += d) {
            paint(i + d / 2, j + d / 2, d, t[((i + N + j + N) / d & 1) + 2]);
        }
    }

    for (int i = 0; i < n; i++) {
        cout << s[i] << "\n";
    }

    return 0;
}