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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;

public static class P
{
    public static void Main()
    {
        var nab = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var n = nab[0];
        var a = nab[1];
        var b = nab[2];
        int[] chunks = Enumerable.Repeat(1, b).ToArray();
        var remain = n - b;
        if (remain < 0)
        {
            Console.WriteLine(-1);
            return;
        }
        for (int i = 0; i < chunks.Length; i++)
        {
            var adder = Min(a - chunks[i], remain);
            chunks[i] += adder;
            remain -= adder;
        }
        if (remain != 0 || chunks.Max() != a)
        {
            Console.WriteLine(-1);
            return;
        }
        int curMax = n;
        List<int> res = new List<int>();
        foreach (var chunk in chunks)
        {
            var start = curMax - chunk + 1;
            res.AddRange(Enumerable.Range(start, chunk));
            curMax = start - 1;
        }

        Console.WriteLine(string.Join(" ", res));
    }
}