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)

import java.util.Scanner;

public class Main {

		public static void main(String[] args) {

			Scanner sc=new Scanner(System.in);
			int n=sc.nextInt();
			int a=sc.nextInt();
			int b=sc.nextInt();
			
			if(a+b>=n+2||a+b<n/3) {
				System.out.println(-1);
				return;
			}
			if(a==1) {
				if(n>1&&b==1) {
					System.out.println(-1);
					return;
				}
				for(int i=n;i>n-b+1;i--) {
					System.out.print(i+" ");
				}
				for(int i=1;i<=n-b+1;i++) {
					System.out.print(i+" ");
				}
				
				return;
			}
			
			for(int i=b;i>=1;i--) {
				System.out.print(i+" ");
			}
			for(int i=n-a+2;i<=n;i++) {
				System.out.print(i+" ");
			}
			for(int i=n-a+1;i>b;i--) {
				System.out.print(i+" ");
			}
			
		}
	}