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<stdio.h>
#define rep(i,n) for(int i=0;i<(int)(n);++i)
int n,a,b,memo[300001]={1};

main() {
    scanf("%d%d%d",&n,&a,&b);
    if (n > 1LL*a*b || n < a+b-1) puts("-1");
    else {
        int now=b,cnt=n;
        while(1) {
            for(int i=0;i<b;++i){
                if (a == cnt) {
                    for(int k=0;k<=n;++k)if (!memo[k]) printf("%d ",k);
                    return 0;
                }
                cnt--;
                printf("%d ",now-i);
                memo[now-i] = 1;
            }
            a--;
            now = n<now+b?n:now+b;
        }
    }
}