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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val N, A, B = sc.nextInt
  val X = N - A - B

  // A + B > N + 1 のとき実現不可能
  if ((A + B) > (N + 1) | N > A * B) {
    println(-1)
    sys.exit
  }

  // それ以外のとき、実現可能
  var arr = Array.emptyIntArray

  if (B != N) {
    for (i <- 1 to A) arr :+= i
  }

  if (A != N) {
    for (j <- N - B + 1 to N) arr +:= j
  }

  if (A > B) {
    for (k <- A + 1 to N - B) arr +:= k
  } else {
    for (k <- N - B to A + 1 by -1) arr +:= k
  }


  println(arr.mkString(" "))
}