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 Python (3.4.3) (judge verdict: Accepted)

N, A, B = map(int, input().split())
if A*B < N or A+B-1 > N:
    print(-1)
else:
    array = [i for i in reversed(range(1, N+1))]
    if A > 1:
        f = array[:B]
        r = array[B:]
        L = [f]
        span = len(r)//(A-1)
        rem = len(r)%(A-1)
        i = 0
        for _ in range(A-1):
            if rem > 0:
                L.append(r[i:i+span+1])
                rem -= 1
                i += span + 1
            else:
                L.append(r[i:i+span])
                i += span
        array = []
        for l in reversed(L):
            array += l
    print(' '.join([str(a) for a in array]))