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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
  val (n, a, b)= readLine()!!.split(" ").map(String::toInt)
  if (a == 1) {
    if (b == n) {
      println((1..n).toList().joinToString(" "))
      return
    } else {
      println(-1)
      return
    }
  }
  if (b == 1) {
    if (a == n) {
      println((n downTo 1).toList().joinToString(" "))
      return
    } else {
      println(-1)
      return
    }
  }

  if (a + b > n + 1) {
    println(-1)
    return
  }

  if (a.toLong() * b.toLong() < n.toLong()) {
    println(-1)
    return
  }

  val ys = IntArray(a)
  ys[0] = b
  for (k in 0 until (n - b)) {
    ys[k % (a - 1) + 1]++
  }

  val xs = mutableListOf<Int>()
  var base = 0
  for (y in ys) {
    for (x in base + y downTo base + 1) {
      xs.add(x)
    }
    base += y
  }
  println(xs.joinToString(" "))
}