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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;
typedef long long ll;

int main()
{
    ll n, a, b;
    cin >> n >> a >> b;
    if(a * b < n || a + b > n + 1){
        cout << -1 << endl;
        return 0;
    }
    int c, e;
    for(c = 0; c < n; c++){
        if(c * a + b - c > n){
            c--;
            e = n - c * a - (b - c - 1);
            break;
        }
    }
    if(a * b == n){
        c = b;
        e = 0;
    }
    for(int i = 0; i < c; i++){
        for(int j = 0; j < a; j++) cout << n - (i + 1) * a + j + 1 << " ";
    }
    for(int j = 0; j < e; j++) cout << n - c * a - e + j + 1 << " ";
    for(int j = n - c * a - e; j > 0; j--) cout << j << " ";
    cout << endl;
}