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.

<image>

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;
const int N = 1e6 + 5;
int n;
int T;
long long a, b;
long long all(long long e) { return e * (e + 1) / 2; }
long long As(long long s, long long e) { return (e - s + 1) * a; }
long long Bs(long long s, long long e) {
  long long start = all(s - 2);
  long long _end = all(e - 1);
  if (s - 2 < 0) start = 0;
  return (_end - start) * b;
}
int main() {
  cin >> a >> b >> T;
  while (T--) {
    long long l, t, m;
    cin >> l >> t >> m;
    long long s = l, e = 1e9;
    while (s < e) {
      long long mid = (s + e + 1) >> 1;
      if (As(l, mid) + Bs(l, mid) <= t * m &&
          As(mid, mid) + Bs(mid, mid) <= t) {
        s = mid;
      } else {
        e = mid - 1;
      }
    }
    if (As(l, s) + Bs(l, s) <= t * m && As(l, l) + Bs(l, l) <= t) {
      cout << s << "\n";
    } else {
      cout << "-1\n";
    }
  }
}
