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: Time Limit Exceeded)

h, w, d = gets.split.map(&:to_i)
a = Hash.new -1
a[[0,0]] = 0
t = d.succ.times.map{|i|
  [d - i, i]
}
t += t.map{|x, y|[-x, y]}
t += t.map{|x, y|[x, -y]}
t.uniq!

h.times { |j|
  w.times { |i|
    t.each { |d|
      x, y = i + d[0], j + d[1]
      next if a[[x, y]] != -1
      next if x < 0 || y < 0 || x >= w || y >= h
      c = []
      t.each { |dd|
        xx, yy = x + dd[0], y + dd[1]
        next if xx < 0 || yy < 0 || xx >= w || yy >= h
        c << a[[xx, yy]]
      }
      a[[x, y]] = ([0, 1, 2, 3] - (c.uniq - [-1]))[0]
    }
  }
}

b = Array.new(h).map{Array.new(w)}
cl = {0=>'R', 1=>'G', 2=>'B', 3=>'Y'}
a.each{|k, v|

  b[k[1]][k[0]] = cl[v]
}

b.each{|b_|
  puts b_ * ''
}