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;

static class Program
{
    static int[] Solve(int N, int A, int B)
    {
        if ((N + A - 1) / A != B) { return null; }
        var ans = new List<int>();
        for (int i = 1; i <= B; ++i)
        {
            int s = N - i * A;
            for (int j = 1; j <= A; ++j)
            {
                if (s + j > 0) { ans.Add(s + j); }
            }
        }
        return ans.ToArray();
    }

    static void Main(string[] args)
    {
        var V = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var ans = Solve(V[0], V[1], V[2]);
        Console.WriteLine((ans != null) ? string.Join(" ", ans) : "-1");
    }
}