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 Ruby (2.3.3) (judge verdict: Runtime Error)

H, W, D = gets.split.map(&:to_i)

def dist(p1, p2)
  (p1[0] - p2[0]).abs + (p1[1] - p2[1]).abs
end

def kai(a, b, c)
  r = Math.sqrt(b**2 - 4 * a * c)
  [(-b + r).fdiv(2 * a), (-b - r).fdiv(2 * a)].uniq
end

msm = Array.new(H) { Array.new(W) { 0 } }

H.times do |h|
  W.times do |w|
    colors = ['R', 'Y', 'G', 'B']
    # [h, w] から D だけ離れているマスを探す。
    0.upto(h) do |dh|
      # dh 行目では？
      x = kai(1, -2 * w, w**2 - ((h - dh).abs - D)**2)
      #puts "(#{h},#{w})から#{D}離れてるマスは…"
      x.each do |xa|
        if (xa % 1) == 0.0 && xa >= 0
          #puts "  (#{dh},#{xa.to_i})"
          colors -= [msm[dh][xa.to_i]]
        end
      end
    end
    if colors.empty?
      p msm
      abort
    else
      msm[h][w] = colors[0]
    end
  end
end

puts msm.map(&:join).join("\n")