Problem: 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.

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.

Examples

Input

5 3 2


Output

2 4 1 5 3


Input

7 7 1


Output

1 2 3 4 5 6 7


Input

300000 300000 300000


Output

-1

Solution (in CPP):

Solution:
#include <cstdio>
#include <queue>
using namespace std;

vector<int> ans;
int main(){
	int N,A,B; scanf("%d %d %d",&N,&A,&B);
	if(N<A) return !printf("-1");
	for(int i=N-A+1;i<=N;i++) if(i>0){
		ans.push_back(i);
	}
	N-=A;
	B--;
	if(B){
		int k=(N+B-1)/B;
		int r=N%B;
		if(!r) r=B;
		if(k>A || !k) return !printf("-1");
		while(B--){
			int gap=k-(r>0 ? 0:1);
			if(!gap) return !printf("-1");
			for(int i=N-gap+1;i<=N;i++) if(i>0){
				ans.push_back(i);
			}
			N-=gap;
			r--;
		}
	}
	if(N>0) return !printf("-1");
	for(int x : ans) printf("%d ",x);
}