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 arc091_c
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
            if (x[0] < x[1] + x[2] - 1 || x[1] * x[2] > x[0]) Console.WriteLine(-1);
            else
            {
                bool rev = false;
                if (x[1] > x[2])
                {
                    rev = true;
                    int hoge = x[1]; x[1] = x[2]; x[2] = hoge;
                }
                var a = new List<int>();
                for (int i = 0; i < x[1]; i++) a.Add(x[0] - (x[1] - i - 1));
                var b = new List<int>();
                int j = 0;
                for (; j <= x[0] - (x[1] + x[2]); j++) b.Add(j + 1);
                var c = new List<int>();
                for (int i = 1; i < x[2]; i++)
                {
                    j++; c.Add(j);
                }
                var cc = c.ToArray(); Array.Reverse(cc);
                a.AddRange(b); a.AddRange(cc);
                var ret = a.ToArray();
                if (rev) Array.Reverse(ret);
                Console.Write(ret[0]);
                for (int i = 1; i < x[0]; i++) Console.Write(" " + ret[i]);
                Console.WriteLine();
            }
        }
    }
}