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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <cmath>
#include <iostream>
#include <vector>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <bitset>
#include <algorithm>
#include <functional>
#include <utility>
#include <iomanip>

#define int long long int
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((int)(x).size())
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )

using namespace std;

typedef pair<int, int> P;

const int INF = 1e15;
const int MOD = 1e9+7;

signed main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n, a, b;
    cin >> n >> a >> b;

    if(a + b > n + 1){
        cout << -1 << endl;
        return 0;
    }

    vector<int> ans;
    for(int i = n - a + 1; i <= n; i++){
        ans.push_back(i);
    }

    int m = n + 1 - a - b;
    for(int i = 1; i <= n + 1 - a - b; i++){
        ans.push_back(i);
    }

    for(int i = n - a; i > m; i--){
        ans.push_back(i);
    }

    cout << ans[0];
    for(int i = 1; i < n; i++){
        cout << " " << ans[i];
    }
    cout << endl;

    return 0;
}