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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.io.PrintWriter;

class Main{
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        long N = scan.nextLong();
        long A = scan.nextLong();
        long B = scan.nextLong();

        if(A+B-1>N || A*B<N){
            System.out.println(-1);
            return;
        }

        List<Long> ansList = new ArrayList<>();
        long n=0,m=0,l=0;
        n=(N-A)/(B-1);
        m=A-n-1;
        l=N-n*B-m;
        // for(int i=1;i<=N;++i){
        //     if(N-i*B <= (A-i-1)+B){
        //         n=i;
        //         m=A-i-1;
        //         l=N-n*B-m;
        //         break;
        //     }
        // }



        for(long i=0;i<n;++i){
            for(long j=B;j>0;--j)ansList.add(i*B+j);
        }
        for(long i=n*B+l;i>n*B;--i)ansList.add(i);
        for(long i=n*B+l+1;i<=N;++i)ansList.add(i);
        PrintWriter pw = new PrintWriter(System.out);
        for(int i=0;i<N;++i)pw.print(ansList.get(i)+(i==N-1 ? "\n":" "));
        pw.flush();pw.close();
    }
}