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)

# coding: utf-8
import sys

sr = lambda: sys.stdin.readline().rstrip()
ir = lambda: int(sr())
lr = lambda: list(map(int, sr().split()))

N, A, B = lr()
if A + B - 1 > N:
    print(-1); exit()

if A * B < N:
    print(-1); exit()

answer = []
for i in range(N-A+1, N+1):
    answer.append(i)

if B > 1:
    start = N-A
    q, r = divmod(N-A, B-1)
    add = [x for x in range(start-r, start+1) if x > 0]
    answer += add
    start -= r + 1
    for i in range(B-1):
        limit = start - i * q
        add = [x for x in range(limit-q+1, limit+1) if x > 0]
        answer += add

print(*answer)