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, c, l, t, m;
bool f(long long mid) {
  long long lo = a * (l - 1) + b * ((l - 1) * (l - 2) >> 1);
  long long hi = a * (mid) + b * (mid * (mid - 1) >> 1);
  long long top = a + b * (mid - 1);
  lo = max(0ll, lo);
  return ((hi - lo <= t * m) && (top <= t));
}
int main() {
  while (cin >> a >> b >> c) {
    for (int i = 0; i < c; i++) {
      cin >> l >> t >> m;
      long long lo = 0, hi = 100000000LL;
      if (a + b * (l - 1) > t) {
        cout << -1 << endl;
        continue;
      }
      while (hi - lo > 1) {
        int mid = (hi + lo) >> 1;
        if (f(mid))
          lo = mid;
        else
          hi = mid;
      }
      if (f(hi))
        cout << hi << endl;
      else
        cout << lo << endl;
    }
  }
}
