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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

set <int> ram;

bool ramas()
{
    return ram.size() > 0;
}

int small()
{
    int x = *ram.begin();
    ram.erase(x);
    return x;
}
int big()
{
    int x = *prev(ram.end());
    ram.erase(x);
    return x;
}

int main()
{
    int n, a, b;
    cin >> n >> a >> b;

    if (a + b - 1 > n || (a == 1 && b != n) || (b == 1 && a != n)) {
        cout << -1;
        return 0;
    }

    for (int i(1); i <= n - a - b + 1; i++)
        ram.insert(i);

    vector <vector <int>> subsir_cresc;

    for (int i(0); i < a; i++) {
        if (!ramas())
            break;
        int l = b - 1 + (i == 0);
        vector <int> sir;
        while (l > 0) {
            l--;
            if (!ramas())
                break;
            sir.push_back(big());
        }
        subsir_cresc.push_back(sir);
    }
    for (int i(0); i < b; i++) {
        if (!ramas())
            break;
        int l = a - 1 + (i == b - 1);
        vector <int> sir;
        while (l--) {
            if (!ramas())
                break;
            sir.push_back(small());
        }
        reverse(sir.begin(), sir.end());
        subsir_cresc.push_back(sir);
    }

    if (ramas()) {
        cout << -1;
        return 0;
    }
    reverse(subsir_cresc.begin(), subsir_cresc.end());

    for (int i(1); i <= a; i++) {
        if (!subsir_cresc.empty()) {
            for (auto j : subsir_cresc.back())
                cout << j << ' ';
            subsir_cresc.pop_back();
        }
        cout << n - (a - i) << ' ';
    }

    for (int i(1); i < b; i++) {
        if (!subsir_cresc.empty()) {
            for (auto j : subsir_cresc.back())
                cout << j << ' ';
            subsir_cresc.pop_back();
        }
        cout << n - a - i + 1 << ' ';
    }

        if (!subsir_cresc.empty()) {
            for (auto j : subsir_cresc.back())
                cout << j << ' ';
            subsir_cresc.pop_back();
        }
    return 0;
}