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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

int n, m, d;
uint8_t a[505][505];

inline int aps(int x) {
	return x < 0 ? -x : x;
}

inline bool valid(int i, int j) {
	for (int x=-d; x<=d; x++) {
		for (int y=-d; y<=d; y++) {

			int u = i+x;
			int v = j+y;

			if (aps(u-i) + aps(v-j) != d) {
				continue;
			}

			if (u >= 1 && v >= 1 && u <= n && v <= m) {
				if (a[u][v] == a[i][j]) {
					return false;
				}
			}
		}


	}
	return true;
}

vector<pair<int, int>> fig1, fig2;

inline bool ok(int i, int j) {
	return (i > 0 && j > 0 && i <= n && j <= m);
}

template<class T>
void crtaj(const T& fig, int x, int y, int c) {
	for (auto p : fig) {
		int u = p.first + x;
		int v = p.second + y;
		if (ok(u, v)) {
			a[u][v] = c;
		}
	}
}



int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	cerr.tie(nullptr);

	cin >> n >> m >> d;

	memset(a, 4, sizeof(a));

	if (d == 1) {
		for (int i=1; i<=n; i++) {
			for (int j=1; j<=m; j++) {
				a[i][j] = (i+j) % 2;
			}
		}
	} else {
		if (d % 2 == 1) {
			for (int x=-d-2; x<=d+2; x++) {
				for (int y=-d-2; y<=d+2; y++) {
					if (aps(x) + aps(y) <= d/2) {
						fig1.push_back({x, y});
					}

					if (aps(x) + aps(y) < d/2 ||
						aps(x-1) + aps(y) < d/2 ||
						aps(x) + aps(y-1) < d/2 ||
						aps(x-1) + aps(y-1) < d/2)
					{
						fig2.push_back({x, y});
					}
				}
			}

			for (int i=-4*d; i<=n+4*d; i+=d) {
				for (int j=-4*d; j<=m+4*d; j+=d) {
					int c = (i/d + j/d + 16) % 2;
					crtaj(fig1, i, j, c);
				}
			}

			for (int i=-4*d; i<=n+4*d; i+=d) {
				for (int j=-4*d; j<=m+4*d; j+=d) {
					int c = (i/d + j/d + 16) % 2;
					crtaj(fig2, i+d/2, j+d/2, 2 + c);
				}
			}

		} else {

			for (int x=-d-2; x<=d+2; x++) {
				for (int y=-d-2; y<=d+2; y++) {
					if (aps(x) + aps(y) < d/2 ||
						aps(x) + aps(y-1) < d/2)
					{
						fig1.push_back({x, y});
					}

					if (aps(x) + aps(y) < d/2 ||
						aps(x-1) + aps(y) < d/2)
					{
						fig2.push_back({x, y});
					}
				}
			}

			for (int i=-4*d; i<=n+4*d; i+=2*d) {
				for (int j=-4*d; j<=m+4*d; j+=2*d) {

					crtaj(fig1, i, j, 0);
					crtaj(fig1, i+d, j+d, 0);

					crtaj(fig1, i+d-1, j, 1);
					crtaj(fig1, i+d+d-1, j+d, 1);

					
					crtaj(fig2, i+d/2-1, j+d/2+1, 2);
					crtaj(fig2, i-d/2-1, j-d/2+1, 2);

					crtaj(fig2, i+d/2-1, j+d/2+d, 3);
					crtaj(fig2, i-d/2-1, j-d/2+d, 3);
					
				}
			}
		}
	}

	bool invalid = false;

	// validate
	for (int i=1; i<=n; i++) {
		for (int j=1; j<=m; j++) {
			if (!valid(i, j)) {
				invalid = true;
			}
		}
	}

	if (invalid) {
		cerr << "invalid\n";
	}

	for (int i=1; i<=n; i++) {
		for (int j=1; j<=m; j++) {
			cout << "RGBY "[a[i][j]];
		}
		cout << '\n';
	}
}