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 (3.8.2) (judge verdict: Wrong Answer)

n,a,b=map(int,input().split())
if a==1:
  if b!=n:print(-1)
  else:print(*[n-i for i in range(n)])
  exit()
if b==1:
  if a!=n:print(-1)
  else:print(*[i+1 for i in range(n)])
  exit()
if a+b-1>n:exit(print(-1))
ans=[]
s=set()
for i in range(n):s.add(i+1)
for i in range(a-1):
  ans.append(i+1)
  s.discard(i+1)
ans.append(n)
s.discard(n)
for i in range(b-2):
  ans.append(n-1-i)
  s.discard(n-1-i)
ans.append(a)
s.discard(a)
l=list(s)
l.sort(reverse=1)
for i in range(len(l)):
  ans.append(l[i])
  ans.append(l[-i-1])
print(*ans[:n])