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<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
void File(){
	freopen("E.in","r",stdin);
	freopen("E.out","w",stdout);
}
#define REP(i,a,b) for(register int i=a;i<=b;++i)
#define DREP(i,a,b) for(register int i=a;i>=n;--i)
#define ll long long
const int maxn=1e6+10;
ll n,a,b;
int s[maxn];
int main(){
	//File();
	cin>>n>>a>>b;
	if(n>a*b || n<a+b-1)
		cout<<-1<<endl;
	else{
		REP(i,1,a)s[i]=n-a+i;
		if(b!=1){
			ll unit=(n-a)/(b-1),res=(n-a)%(b-1);
			int p=a,from=n-a-unit+1,last=n-a;
			while(p!=n){
				if(res)--res,--from;
				REP(i,from,last)
					s[++p]=i;
				last=from-1;
				from=from-unit;
			}
		}
		REP(i,1,n)cout<<s[i]<<" ";
	}
	return 0;
}