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: Runtime Error)

using System;
using System.Linq;
using System.Diagnostics;
using System.Collections.Generic;
class P
{
    static void Main()
    {
        int[] nab = Console.ReadLine().Split().Select(int.Parse).ToArray();
        //LDSは逆からのLIS
        if (nab[1] + nab[2] - 1 > nab[0] || nab[0] >= (nab[1] + nab[2] - 1) * 2)
        {
            Console.WriteLine(-1);
        }
        else
        {
            //核となる数字を決める。(全体のa:bくらいに基点を置きたい)
            int core = (int)Math.Ceiling(nab[2] * ((double)nab[0] / (nab[1] + nab[2])));

            //LIS生成
            int[] lis = new int[nab[1]];
            for (int i = 0; i < nab[1]; i++)
            {
                lis[i] = nab[0] - nab[1] + i + 1;
            }
            //LDS生成
            int[] lds = new int[nab[2]];
            for (int i = 0; i < nab[2]; i++)
            {
                lds[i] = nab[2] - i;
            }
            //ダミーLIS生成(コアの上の数個)
            int[] dlis = new int[lis[0] - core - 1];
            for (int i = 0; i < dlis.Length; i++)
            {
                dlis[i] = core + i + 1;
            }
            //ダミーLDS生成(コアの上の数個)
            int[] dlds = new int[core - lds[0] - 1];
            for (int i = 0; i < dlis.Length; i++)
            {
                dlis[i] = core - i - 1;
            }
            int[] res = new int[nab[0]];
            res[0] = core;
            int index = 1;
            lis.CopyTo(res, index);
            index += lis.Length;
            lds.CopyTo(res, index);
            index += lds.Length;
            dlis.CopyTo(res, index);
            index += dlis.Length;
            dlds.CopyTo(res, index);
            if(res.Distinct().Count() != res.Length)
            {
                RE();
            }
            Console.WriteLine(string.Join(" ", res));
        }
    }
    static void WA()
    {
        Console.WriteLine("WA");
    }
    static void TLE()
    {
        for (long i = 0; i < long.MaxValue; i++) ;
    }
    static void MLE()
    {
        int a = new int[int.MaxValue].Sum();
    }
    static void RE()
    {
        int a = (new int[0])[10];
    }
}