Problem:
Score : 700 points

Problem Statement

Determine if there exists a sequence obtained by permuting 1,2,...,N that satisfies the following conditions:

The length of its longest increasing subsequence is A.

The length of its longest decreasing subsequence is B.

If it exists, construct one such sequence.

Notes

A subsequence of a sequence P is a sequence that can be obtained by extracting some of the elements in P without changing the order.

A longest increasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically increasing.

Similarly, a longest decreasing subsequence of a sequence P is a sequence with the maximum length among the subsequences of P that are monotonically decreasing.

Constraints

1 \leq N,A,B \leq 3\times 10^5

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

If there are no sequences that satisfy the conditions, print -1.

Otherwise, print N integers. The i-th integer should be the i-th element of the sequence that you constructed.

Sample Input 1

5 3 2

Sample Output 1

2 4 1 5 3

One longest increasing subsequence of this sequence is {2,4,5}, and one longest decreasing subsequence of it is {4,3}.

Sample Input 2

7 7 1

Sample Output 2

1 2 3 4 5 6 7

Sample Input 3

300000 300000 300000

Sample Output 3

-1

Solution in Ruby (2.3.3) (judge verdict: Accepted)

N,A,B = gets.split.map(&:to_i)

begin
  fail if A*B < N
  ss = [B]
  nn = N - B
  fail if nn < 0
  if A == 1
    fail if nn > 0
  else
    fail if nn == 0
    a = A-1
    while a > 0
      fail if nn < a
      if nn % a == 0 && nn/a<= B
        ss += Array.new(a, nn/a)
        break
      end
      r = [B, nn - (a-1)].min
      ss << r
      nn -= r
      a -= 1
    end
    #p [ss.size, ss.inject(:+), ss[-3..-1]]

    
  end
  #p ss.inject(:+)
  arr = (1..N).to_a
  t = 0
  ss.each{ |s|
    if s > 1
      arr[t,s] = arr[t,s].reverse
    end
    t += s
  }
  puts arr.join(" ")
rescue => e
  $stderr.puts e
  p -1; exit
end