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 (GCC 5.4.1) (judge verdict: Accepted)

int n,a,b,M[1<<20]={1},i,k;
main(){
    scanf("%d%d%d",&n,&a,&b);
    if(n>1L*a*b||n<a+b-1) puts("-1");
    else{
        int N=b,C=n;
        while(1){
            for(i=0;i<b;++i) {
                if(a==C){
                    for(k=0;k<=n;++k) if(!M[k]) printf("%d ",k);
                    exit(0);
                }
                C--;printf("%d ",N-i);M[N-i]=1;
            }
            a--;
            N=n<N+b?n:N+b;
        }
    }
}