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:
import math
#import numpy as np
import queue
from collections import deque,defaultdict
import heapq as hpq
from sys import stdin,setrecursionlimit
#from scipy.sparse.csgraph import dijkstra
#from scipy.sparse import csr_matrix
ipt = stdin.readline
setrecursionlimit(10**7)

def main():
    n,a,b = map(int,ipt().split())
    if a*b < n or a+b-1 > n:
        print(-1)
        exit()
    ans = [str(b-i) for i in range(b)]
    si = n-a+2
    ue = n+1
    i = 0
    while True:
        if si <= b or a == 1:
            break
        ans[i] += " "+" ".join(map(str,range(si,ue)))
        ue = si
        si -= a-1
        i += 1
    if i < b and b+1 < ue:
        ans[i] += " "+" ".join(map(str,range(b+1,ue)))
    print(" ".join(ans))
    return

if __name__ == '__main__':
    main()