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: Wrong Answer)

n, a, b = map(int, input().split())

if a == 1 and b == 1 and n == 1:
    print('1')
elif a == 1:
    if b == n:
        print(' '.join(list(map(str, reversed(range(1, n+1))))))
    else:
        print('-1')
elif b == 1:
    if a == n:
        print(' '.join(list(map(str, range(1, n+1)))))
    else:
        print('-1')
elif a + b - 1 > n:
    print('-1')
else:
    inc = ' '.join(list(map(str, range(n-a+1, n+1))))
    dec = ' '.join(list(map(str, reversed(range(1, b)))))
    other1 = list(map(str, range(n-a, b-1, -2)))
    other2 = list((map(str, reversed(range(n-a-1, b-1, -2)))))
    if len(other1) == len(other2):
        other = ' '.join(['{} {}'.format(other1[i], other2[i]) for i in range(len(other1))])
    else:
        length = len(other2)
        other1 = other1[::-1]
        other2 = other2[::-1]
        other = other1[-1] + ' ' + ' '.join(['{} {}'.format(other1[i], other2[i]) for i in range(length)])

    ans = inc + ' ' + dec + ' ' + other
    print(ans)