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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<cstdio>
using namespace std;
int n,a,b,p,rl,lr;
void solve(int l,int r)
{
	rl=r-a+1;
	if (rl<=l)
	{
		for (int i=l;i<=r;i++) printf("%d ",i);
		return;
	}
	for (int i=rl;i<=r;i++) printf("%d ",i);
	lr=l+b-1;
	if (lr>=rl)
	{
		for (int i=l;i<=rl-1;i++) printf("%d ",i);
		return;
	}
	for (int i=l;i<=lr;i++) printf("%d ",i);
	solve(lr+1,rl-1);
}
int main()
{
	scanf("%d%d%d",&n,&a,&b);
	if (a+b>n+1) 
	{
		printf("-1\n");
		return 0;
	}
	solve(1,n);
	return 0;
}