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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

/*
 * 1,2,…,N を並べ替えてできる列であって、以下の条件を満たすものがあるかどうか判定し、あればその例をひとつ構成してください。
 * 
 *     最長増加部分列の長さは A である
 *     最長減少部分列の長さは B である
 */

import java.util.*;
	public class Main{
		public static void main(String[] args){
            Scanner sc = new Scanner(System.in);
            //入力
            int n = Integer.parseInt(sc.next());
            int a = Integer.parseInt(sc.next());
            int b = Integer.parseInt(sc.next());
            
            if(n < a+b-1 || a*b < n){
            	System.out.println(-1);
            	sc.close();
            	return;
            }else if(b==1){
            	System.out.print(1);
            	
            	for(int i=1; i<n; i++){
        			System.out.print(" " + (i+1));
        		}
            	sc.close();
            	return;
            }
            
            int set = (n-a-b+1)/(b-1), remain = (n-a-b+1)%(b-1);
            
            for(int i=0; i<b; i++){
            	if(i==0){
            		System.out.print(b);
            		for(int j=1; j<a; j++){
            			if(j<set+1){
            				System.out.print(" " + (b*(j+1)));
            			}else{            			
            				System.out.print(" " + (b*(set+1) + remain + j - set));
            			}
            		}
            	}else if(i<=remain){
            		for(int j=0; j<set+1; j++){
            			System.out.print(" " + (b*(j+1)-i));
            		}
            		System.out.print(" " + (b*(set+1) - i + remain + 1));
            	}else{
            		for(int j=0; j<set+1; j++){
            			System.out.print(" " + (b*(j+1)-i));
            		}
            	}
            }
            
            System.out.println("");
            sc.close();
		}
    }