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, n, l, t, m;
bool check(long long x) {
  long long n = x - l + 1;
  long long a1 = A + B * (l - 1);
  long long an = A + B * (x - 1);
  long long sum = (a1 + an) * n / 2;
  return sum <= t * m && an <= t;
}
int binary() {
  long long le = l, ri = t;
  while (le + 1 < ri) {
    int mid = (le + ri) >> 1;
    if (check(mid))
      le = mid;
    else
      ri = mid;
  }
  if (!check(le)) return -1;
  return check(ri) ? ri : le;
}
int main() {
  ios::sync_with_stdio(false);
  cin >> A >> B >> n;
  while (n--) {
    cin >> l >> t >> m;
    cout << binary() << endl;
  }
  return 0;
}
