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 PYTHON):

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

if (N+B-1)/B <= A <= N+1-B:
  L = [A] + [1]*(B-1)
  n = N - A - (B-1)
  for i in range(1, B):
    L[i] += min(n, A-1)
    n -= min(n, A-1)
  T = [[] for _ in range(B)]
  p = 0
  for i in range(1,N+1):
    while len(T[p]) >= L[p]:
      p += 1
    T[p] += [i]
  for t in T[::-1]:
    for x in t:
      print x,
  print
else:
  print -1


"""
from itertools import *

# http://wakabame.hatenablog.com/entry/2017/08/27/210846
def LIS(L):
  N = len(L)
  res=0
  dp=[1]*N
  for i in range(N):
    for j in range(i):
      if L[j]<L[i]:
        dp[i]=max(dp[i],dp[j]+1)
    res=max(res,dp[i])
  return res

n = 3
# ..o
# .o.
# o..

n = 4
# ...o
# .oo.
# .o..
# o...

n = 5
# ....o
# ..oo.
# .oo..
# .o...
# o....

n = 6
# .....o
# ..ooo.
# .ooo..
# .oo...
# .o....
# o.....

n = 7
# ......o
# ...ooo.
# ..ooo..
# .ooo...
# .oo....
# .o.....
# o......

n = 8
# .......o
# ...oooo.
# ..oooo..
# .oooo...
# .ooo....
# .oo.....
# .o......
# o.......

n = 9
# ........o
# ....oooo.
# ..ooooo..
# ..oooo...
# .oooo....
# .ooo.....
# .oo......
# .o.......
# o........

n = 10
# .........o
# ....ooooo.
# ...ooooo..
# ..ooooo...
# .ooooo....
# .oooo.....
# .ooo......
# .oo.......
# .o........
# o.........


T = [["."]*(n+1) for _ in range(n+1)]

for x in permutations(range(1,n+1)):
  #print x, LIS(x), LIS(x[::-1])
  T[LIS(x)][LIS(x[::-1])] = "o"

for t in T[1:]:
  print "".join(t[1:])

"""