Problem: 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.

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.

Examples

Input

5 3 2


Output

2 4 1 5 3


Input

7 7 1


Output

1 2 3 4 5 6 7


Input

300000 300000 300000


Output

-1

Solution (in PYTHON3):

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

if N < (A + B - 1) or 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))