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)

def solve(N, A, B):
    if N < A + B - 1:
        return None
    
    a = max(A, B)
    b = min(A, B)
    
    if b == 1:
        if a == N:
            ans = list(range(1, N+1))
        else:
            return None
    elif b == 2:
        if 2 * a >= N:
            a_lst = list(range(N-a+1, N+1)) # total A element
            c_lst = list(range(1, N-a+1)) # remaining
            ans = []
            for i in range(len(a_lst)):
                ans.append(a_lst[i])
                if i < len(c_lst):
                    ans.append(c_lst[i])
        else:
            return None
    else:
        a_lst = list(range(N-a+1,N+1)) # total A element. N-A+1 is assured to be greater than 1.
        b_lst = list(range(1, min(N-a, a))) # maximum A element
        c_lst = list(range(min(N-a, a), N-a+1)) # at least one element
        
        ans = []
        for i in range(len(a_lst)):
            ans.append(a_lst[i])
            if i < len(c_lst):
                ans.append(c_lst[i])
        for i in range(b - 2):
            ans.append(b_lst[b-3-i])
        for i in range(b - 2, len(b_lst)):
            ans.append(b_lst[i])
    
    if A >= B:
        return ans
    else:
        return [N+1-i for i in ans]

N, A, B = map(int, input().split())
ans = solve(N, A, B)
if ans is None:
    print(-1)
else:
    for i in ans:
        print(i, end=' ')
    print()