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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ARC091E
{
    class Program
    {
        static void Main(string[] args)
        {
            var line1 = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = line1[0];
            int A = line1[1];
            int B = line1[2];

            
            if (A + B > N + 1)
            {
                Console.WriteLine("-1");
            }
            else
            {
                List<int> ans = new List<int>();

                List<int> nums = new List<int>();
                for (int i = 0; i < N; i++) nums.Add(i + 1);
                while (true)
                {
                    if (nums.Count <= A - 1)
                    {
                        ans.AddRange(nums);
                        break;
                    }
                    ans.AddRange(nums.Take(A - 1));
                    nums = nums.Skip(A - 1).ToList();

                    if (nums.Count <= B - 1)
                    {
                        ans.AddRange(nums);
                        break;
                    }
                    ans.AddRange(nums.Skip(nums.Count - (B - 1)));
                    nums = nums.Take(nums.Count - (B - 1)).ToList();
                }

                Console.WriteLine(string.Join(" ", ans));
            }
            Console.ReadKey();

        }
    }
}