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: Runtime Error)

#include "bits/stdc++.h"
using namespace std;
using ll     = long long;
using pii    = pair<int, int>;
using pll    = pair<ll, ll>;
using vi     = vector<int>;
using vl     = vector<ll>;
using vvi    = vector<vi>;
using vvl    = vector<vl>;
const ll INF = 1LL << 60;
const ll MOD = 1000000007;
template <class T>
bool chmax(T &a, const T &b) {
    return (a < b) ? (a = b, 1) : 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    return (b < a) ? (a = b, 1) : 0;
}
template <class C>
void print(const C &c, std::ostream &os = std::cout) {
    std::copy(std::begin(c), std::end(c), std::ostream_iterator<typename C::value_type>(os, " "));
    os << std::endl;
}

int main() {
    ll n, a, b;
    cin >> n >> a >> b;
    if (a + b - 1 > n) {
        cout << -1 << "\n";
        return 0;
    }
    if (a * b < n) {
        cout << -1 << "\n";
        return 0;
    }
    vi arr(a * b, 0);
    int val = 0;
    for (int i = 0; i < a * b; ++i) {
        arr[i] = val++;
        if (i % a == a - 1) {
            val -= 2 * a;
        }
    }
    vi subseq;
    int to_add = n - a - b + 1;
    for (int i = 0; i < a * b; ++i) {
        if (i < a || i % a == a - 1)
            subseq.push_back(arr[i]);
        else if (to_add > 0) {
            subseq.push_back(arr[i]);
            to_add--;
        }
    }
    vi sorted = subseq;
    sort(sorted.begin(), sorted.end());
    for (int i = 0; i < n; ++i) {
        cout << 1 + lower_bound(sorted.begin(), sorted.end(), subseq[i]) - sorted.begin() << " ";
    }
    cout << endl;
    return 0;
}