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)
$table = []
h.times do |i|
  $table[i] = []
  w.times do |j|
    $table[i][j] = nil
  end
end


h.times do |i|
  w.times do |j|
    next if $table[i][j]

  end
end
def remove(i, j, c)
  (0..$d).each do |k|
    [-1, 1].each do |a|
      ii = i+a*k
      next if ii < 0
      next unless $table[ii]
      [-1, 1].each do |b|
        jj = j+b*($d-k)
        next if jj < 0
        next unless $table[ii][jj]
        next if $table[ii][jj] == [c]
        rep = $table[ii][jj].include? c
        $table[ii][jj] -= [c]
        #remove(ii, jj, c) if rep
      end
    end
  end
end
h.times do |i|
  w.times do |j|
    c = $table[i][j].first
    next if $table[i][j].length == 1
    $table[i][j] = [c]
    remove(i, j, c)
  end
end
$table.each do |row|
  row.each do |v|
    print v[0]
  end
  puts ""
end