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 Ruby (2.3.3) (judge verdict: Accepted)

N, A, B = gets.split.map(&:to_i)

if N == 1
    if A == 1 && B == 1
        print 1
    else
        print -1
    end

elsif N == 2
    if A == 2 && B == 1
        print '1 2'
    elsif A == 1 && B == 2
        print '2 1'
    else
        print -1
    end

# 1 2 3 4 5 ...
elsif B == 1
    if A == N
        print (1..N).to_a.join(' ')
    else
        print -1
    end

#####   middle = 3, wide = 13
#####
###
#
#
elsif A + B - 1 <= N && N <= A * B 
    stairs = Array.new(B){Array.new()}
    middle = (N - A + B - 2) / (B - 1)
    wide = N - A + middle
    wide.times do |i|
        stairs[i % B].unshift(N - i)
    end
    stairs[0] = (1..(N - wide)).to_a + stairs[0]
    result = []
    stairs.each_with_index do |stair, i|
        print (i > 0 ? ' ' : ''), stair.join(' ')
    end

else
    print -1 
end