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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>

using namespace std;

int main(){
  long long N,A,B,i;
  cin >> N >> A >> B;
  int a[N];
  if (A>N || B > N || A+B >N+1 || (N+A-1)/A > B) {
    cout << -1;
  } else {
    int m=N+1-A-B;
    for (i=0;i<A;i++) {
      a[i]=N-A+i+1;
    }
    int k=1;
    while (m>=A) {
      for (i=A*k;i<A*(k+1);i++) {
        a[i]=N-(2*A*k)-A+i+1;
      }
      m-=A-1;
      k+=1;
    }
    int j=A*k;
    for (i=j;i<j+m+1;i++) {
      a[i]=N-(A*k)-m+i-j;
    }
    j+=m+1;
    for (i=j;i<N;i++) {
      a[i]=N-i;
    }

    for (i=0;i<N;i++) {
      cout << a[i];
      if (i<N-1) cout << " ";
    }
  }
  return 0;
}