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 main(){
    long int max,min=1,up,down;
    scanf("%d%d%d",&max,&up,&down);
    if(up+down>max+1||((up-1)*(down-1)==0&&up+down-max-1)){
        printf("-1\n");
        return 0;
    }
    for(int i=0;++i-up;){
        printf("%d ",min);
        ++min;
    }
    for(int i=0;++i-down;){
        printf("%d ",max);
        --max;
    }
    for(int i=1;min-max;i++){
        if(i%2){
            printf("%d ",min);
            ++min;
        }
        else{
            printf("%d ",max);
            --max;
        }
    }
    printf("%d\n",min);
}