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: Accepted)

#include <cstdio>
#include <algorithm>

using std::sort;
using std::swap;
using std::lower_bound;
using std::reverse;

const int MAXN=3e5+5;
int n,a,b;
int p[MAXN];

/*inline void construct(){
	static int tmp[MAXN<<1];
	int i=1;
	for(int k=1;k<=a;i+=2,++k)
		tmp[i]=i;
	int lim=i-2;
	i-=2+1;
	if(a+b==n+1) --b;
	for(int k=1;k<=b;i-=2,++k)
		tmp[i]=tmp[i+1]+1;
	for(int i=1;i<=n;++i)
		p[i]=tmp[i];
	sort(tmp+1,tmp+lim+1);
	for(int i=1;i<=n;++i)
		p[i]=lower_bound(tmp+1,tmp+lim+1,p[i])-tmp;
	for(int i=1;(i<<1)<=n;++i)
		tmp[i]=i<<1;
	if(n&1) tmp[(n>>1)+1]=1;
	for(int i=(n>>1)+1+(~n&1),j=n>>1<<1;i<=n;++i)
}*/

int main(){
	scanf("%d%d%d",&n,&a,&b);
	for(int i=1;i<=n;++i)
		p[i]=i;
	if(a+b>n+1 || (n+a-1)/a>b){
		printf("-1");
		return 0;
	}
	if(a==1){
		for(int i=n;i;--i)
			printf("%d ",i);
		return 0;
	}
	int len=(n-b)/(a-1),rest=(n-b)%(a-1);
	//lds:len=b
	reverse(p+1,p+b+1);
	for(int i=2,l=b+1;i<=a;++i){
		if(rest){
			reverse(p+l,p+l+len+1);
			--rest;
			l+=len+1;
		}
		else{
			reverse(p+l,p+l+len);
			l+=len;
		}
	}
	for(int i=1;i<=n;++i)
		printf("%d ",p[i]);
	return 0;
}