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 <cstdio>

int g[500000],h[500000];
int i,j,k,n,t,x,y;

int main()
{
	scanf("%d%d%d",&n,&x,&y);
	for (i=1;i<=x;i++)
		k++,g[k]=n-x+i;
	y--;
	while ((k<n) && (y))
	{
		y--;
		for (j=k+1;(j<=k+x) && (n-j>=y);j++)
			t++,h[t]=n-j+1;
		if (! t)
		{
			puts("-1");
			return 0;
		}
		for (;t>0;t--)
			k++,g[k]=h[t];
	}
	if ((k<n) || (y))
		puts("-1");
	else
		for (i=1;i<=n;i++)
			printf("%d ",g[i]);
	return 0;
}