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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

N, A, B = map(int, input().split())

base = list(range(N, 0, -1))
if A < B:
    tmp = A
    A = B
    B = tmp
    base.reverse()

if (N - 1) // B + 1 <= A <= N - B + 1:
    possible = 1
else:
    possible = 0

if possible:
    split = [A]
    N_left = N - A
    for i in range(B-1, 0, -1):
        split.append((N_left - 1) // i + 1 + split[-1])

    split.insert(0, 0)
    ans = []
    for i in range(1, len(split)):
        rev = base[split[i-1]:split[i]]
        rev.reverse()
        ans.extend(rev)
    print(" ".join(map(str, ans)))
else:
    print(-1)