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 Go (1.6) (judge verdict: Runtime Error)

package main

import (
	"fmt"
	"math"
)

// 2018-08-04T14:42:31+0800
// 2018-08-04T14:54:30+0800
// 2018-08-04T15:27:19+0800 # @see https://arc091.contest.atcoder.jp/submissions/2940934
// 2018-08-04T15:32:40+0800
func main() {
	var N, A, B int
	fmt.Scanf("%d%d%d", &N, &A, &B)
	if A+B > N+1 {
		fmt.Println(-1)
		return
	}
	if false {
		min := 0
		NN := N
		root := 0
		for ; true; {
			root = int(math.Sqrt(float64(NN)))
			NN = NN - root*root
			if NN <= 2 {
				min += NN
				break
			}
			min += root
		}
		if A+B < min {
			fmt.Println(-1)
			return
		}
	} else {
		if A*B < N {
			fmt.Println(-1)
			return
		}
	}
	// Now divide N to A groups while the largest one is B
	// (A-1)*span + B = N
	span := (N - B) / (A - 1)
	left := (N - B) - span*(A-2)
	out := make([]int, N)
	iout := 0
	// span <= span <= B
	for i := 0; i < A-2; i++ {
		for ii := 0; ii < span; ii++ {
			out[iout] = i*span + span - ii
			iout++
		}
	}
	i := A - 2
	for ii := 0; ii < left; ii++ {
		out[iout] = i*span + left - ii
		iout++
	}
	for ii := 0; ii < B; ii++ {
		out[iout] = i*span + left + B - ii
		iout++
	}
	for i := 0; i < N-1; i++ {
		fmt.Print(out[i], " ")
	}
	fmt.Println(out[N-1])
}