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: Runtime Error)

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

if N < A + B - 1 and N > A * B:
	print(-1)
	exit(0)

if B == 1 and A == N:
	seq = [str(n) for n in range(1,N+1)]
	print(' '.join(seq))
	exit(0)

seq = [str(num)for num in range(N-A+1,N+1)]
dif = (A * B - N)
div = A - (dif // (B-1))
mer = (dif % (B-1))

n = N - A
for i in range((B-1) - mer):
	for j in range(n-(div)+1,n+1):
		seq.append(str(j))
	n -= (div)

for i in range(mer):
	for j in range(n-div+2,n+1):
		seq.append(str(j))
	n -= (div + 1)

print(' '.join(seq))