Karafs is some kind of vegetable in shape of an 1 × h rectangle. Tavaspolis people love Karafs and they use Karafs in almost any kind of food. Tavas, himself, is crazy about Karafs.

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Each Karafs has a positive integer height. Tavas has an infinite 1-based sequence of Karafses. The height of the i-th Karafs is si = A + (i - 1) × B.

For a given m, let's define an m-bite operation as decreasing the height of at most m distinct not eaten Karafses by 1. Karafs is considered as eaten when its height becomes zero.

Now SaDDas asks you n queries. In each query he gives you numbers l, t and m and you should find the largest number r such that l ≤ r and sequence sl, sl + 1, ..., sr can be eaten by performing m-bite no more than t times or print -1 if there is no such number r.

Input

The first line of input contains three integers A, B and n (1 ≤ A, B ≤ 106, 1 ≤ n ≤ 105).

Next n lines contain information about queries. i-th line contains integers l, t, m (1 ≤ l, t, m ≤ 106) for i-th query.

Output

For each query, print its answer in a single line.

Examples

Input

2 1 4
1 5 3
3 3 10
7 10 2
6 4 8


Output

4
-1
8
-1


Input

1 5 2
1 5 10
2 7 4


Output

1
2
#include <bits/stdc++.h>
using namespace std;
int main() {
  int i;
  long long A, B, N, L, T, M, s, e, m;
  cin >> A >> B >> N;
  for (i = 0; i < N; i++) {
    cin >> L >> T >> M;
    if (A + B * (L - 1) > T)
      cout << -1 << endl;
    else {
      s = L;
      e = L + T;
      while (e - s > 1) {
        m = (s + e) / 2LL;
        if (A + B * (m - 1LL) <= T &&
            A * (m - L + 1LL) +
                    B * ((m - 1LL) * m / 2LL - (L - 2LL) * (L - 1LL) / 2LL) <=
                T * M)
          s = m;
        else
          e = m;
      }
      cout << s << endl;
    }
  }
  return 0;
}
