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 static System.Console;
using static System.Math;

namespace AtTest._700problems
{
    class ARC091_E
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int[] nab = ReadInts();
            long n = nab[0];
            long a = nab[1];
            long b = nab[2];
            bool reverse = a < b;
            long high = Max(a, b);
            long low = Min(a, b);
            if (a * b < n || n + 1 < a + b)
            {
                WriteLine(-1);
                return;
            }

            long first = n - high + 1;
            List<long> res = new List<long>();
            for(int i = 0; i < high; i++)
            {
                res.Add(first + i);
            }
            if (low > 1)
            {
                long cnt = (first - 1) / (low - 1);
                for (long i = 0; i < b - 1; i++)
                {
                    if (i == b - 2)
                    {
                        for (long j = 1; j < first - i * cnt; j++)
                        {
                            res.Add(j);
                        }
                    }
                    else
                    {
                        for (long j = 0; j < cnt; j++)
                        {
                            res.Add(first - (i + 1) * cnt + j);
                        }
                    }
                }
            }
            for(int i = 0; i < res.Count; i++)
            {
                Write(reverse ? n - res[i] + 1 : res[i]);
                if (i < res.Count - 1) Write(' ');
            }
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}