Problem:
Score : 300 points

Problem Statement

We have a square grid with H rows and W columns.
Snuke wants to write 0 or 1 in each of the squares.
Here, all of the following conditions have to be satisfied:

For every row, the smaller of the following is A: the number of 0s contained in the row, and the number of 1s contained in the row. (If these two numbers are equal, “the smaller” should be read as “either”.)

For every column, the smaller of the following is B: the number of 0s contained in the column, and the number of 1s contained in the column.

Determine if these conditions can be satisfied by writing 0 or 1 in each of the squares. If the answer is yes, show one way to fill the squares so that the conditions are satisfied.

Constraints

1 \leq H,W \leq 1000

0 \leq A

2 \times A \leq W

0 \leq B

2 \times B \leq H

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H W A B

Output

If the conditions cannot be satisfied by writing 0 or 1 in each of the squares, print -1.

If the conditions can be satisfied, print one way to fill the squares so that the conditions are satisfied, in the following format:

s_{11}s_{12}\cdots s_{1W}
s_{21}s_{22}\cdots s_{2W}
\vdots
s_{H1}s_{H2}\cdots s_{HW}

Here s_{ij} is the digit written in the square at the i-th row from the top and the j-th column from the left in the grid.

If multiple solutions exist, printing any of them will be accepted.

Sample Input 1

3 3 1 1

Sample Output 1

100
010
001

Every row contains two 0s and one 1, so the first condition is satisfied.
Also, every column contains two 0s and one 1, so the second condition is satisfied.

Sample Input 2

1 5 2 0

Sample Output 2

01010

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

h, w, a, b = gets.split.map(&:to_i)
h_option_1 = w - a
h_option_2 = w - h_option_1
w_option_1 = h - b
w_option_2 = h - w_option_1
h_min = [h_option_1, h_option_2].min
h_max = [h_option_1, h_option_2].max
h_gap = h_max - h_min
w_min = [w_option_1, w_option_2].min
w_max = [w_option_1, w_option_2].max
w_gap = w_max - w_min
ans = Array.new(h) { Array.new(w) }

h_options = [h_min * h]
h.times do
  h_options << h_options.last + h_gap
end

w_options = [w_min * w]
w.times do
  w_options << w_options.last + w_gap
end

same_options = h_options & w_options

if same_options.empty?
  puts "No"
  exit
else
  same_option = same_options.first
  w_max_count = w_options.bsearch_index { |i| i >= same_option }
  w_min_count = w - w_max_count
  h_max_count = h_options.bsearch_index { |i| i >= same_option }
  h_min_count = h - h_max_count
  h_rest_hash = Hash.new(0)
  tmp = 0
  h_max_count.times do
    h_rest_hash[tmp] = h_max
    tmp += 1
  end
  h_min_count.times do
    h_rest_hash[tmp] = h_min
    tmp += 1
  end

  w_rest_hash = Hash.new(0)
  tmp_2 = 0
  w_max_count.times do
    w_rest_hash[tmp_2] = w_max
    tmp_2 += 1
  end
  w_min_count.times do
    w_rest_hash[tmp_2] = w_min
    tmp_2 += 1
  end

  h_orders = (0..h - 1).to_a
  w_orders = (0..w - 1).to_a

  h_orders.each do |h_index|
    w_orders.each do |w_index|
      # h_index = (h_index + w_index) % h
      w_index = (w_index + h_index) % w
      if h_rest_hash[h_index] > 0 && w_rest_hash[w_index] > 0
        puts h_index
        puts w_index
        ans[h_index][w_index] = 1
        h_rest_hash[h_index] -= 1
        w_rest_hash[w_index] -= 1
      else
        ans[h_index][w_index] = 0
      end
      p h_rest_hash
      p w_rest_hash
      puts ""
    end
  end

  ans.each do |row|
    puts row.join
  end
end