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 PyPy3 (7.3.0) (judge verdict: Accepted)

N,A,B=map(int,input().split())
if A+B-1>N or A*B<N:
  print(-1)
  exit()
Q=[[] for i in range(B)]
for i in range(N):
  Q[i//A].append(i+1)
Q=Q[::-1]
X=N-1
for i in range(B):
  if len(Q[i])==0:
    Q[i].append(Q[-(X//A+1)][-1])
    del Q[-(X//A+1)][-1]
    X-=1
  else:
    break
P=[]
for i in range(B):
  for j in range(len(Q[i])):
    P.append(Q[i][j])
print(*P)