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.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		string[] input = Console.ReadLine().Split(' ');
		long n = long.Parse(input[0]);
		long b = long.Parse(input[1]);
    long a = long.Parse(input[2]);
		bool answer = true;
    long[] answers = new long[n];
    long looked = 0;

    if(a > n) answer = false;
    else if(a+b-1 > n) answer = false;
    else if(a*b < n) answer = false;

    if(!answer) Console.WriteLine(-1);
    else if(b != 1)
    {
      for(long i = 0; i < a; i++)
      {
        answers[i] = a-i;
      }
      looked = a;
      
      long setc = (n-a)/(b-1);
      long restc = (n-a)%(b-1);
      long num = a;

      for(long i = 0; i < restc; i++)
      {
        num += setc+1;
        for(long j = 0; j < setc+1; j++)
        {
          answers[looked] = num-j;
          looked++;
        }
      }

      for(long i = 0; i < b-1-restc; i++)
      {
        num += setc;
        for(long j = 0; j < setc; j++)
        {
          answers[looked] = num-j;
          looked++;
        }
      }

      Console.WriteLine(string.Join(" ", answers));
    }else
    {
      for(long i = 0; i < n; i++) answers[i] = n-i;
      Console.WriteLine(string.Join(" ", answers));
    }
	}
}