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 Lua (5.3.2) (judge verdict: Accepted)

local n, a, b = io.read("*n", "*n", "*n")
local bmax = n + 1 - a
local bmin = math.ceil(n / a)
if n < a or b < bmin or bmax < b then
  print(-1)
else
  local t = {}
  for i = 1, a do
    t[i] = n - a + i
  end
  local curmax = n - a
  local rem = n + 1 - a - b
  while 0 < rem do
    if a - 1 <= rem then
      for i = 1, a do
        table.insert(t, curmax - a + i)
      end
      curmax = curmax - a
      rem = rem - a + 1
    else
      for i = 1, rem + 1 do
        table.insert(t, curmax - rem - 1 + i)
      end
      curmax = curmax - rem - 1
      rem = 0
    end
  end
  for i = curmax, 1, -1 do
    table.insert(t, i)
  end
  print(table.concat(t, " "))
end