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;
long long a, b, q, p, t, m;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> a >> b >> q;
  while (q--) {
    cin >> p >> t >> m;
    long long l = p, r = 2e6, ans = -1;
    while (l <= r) {
      long long mid = (l + r) >> 1;
      if (a + (mid - 1) * b <= t &&
          mid * (a + a + (mid - 1) * b) / 2 -
                  (p - 1) * (a + a + (p - 2) * b) / 2 <=
              m * t) {
        ans = mid;
        l = mid + 1;
      } else {
        r = mid - 1;
      }
    }
    cout << ans << "\n";
  }
}
