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;
long long l, t, m;
long long verify(long long r) {
  if (A + (r - 1) * B > t) return 0;
  if (A * (r - l + 1) + B * ((r * (r - 1)) / 2 - ((l - 1) * (l - 2)) / 2) >
      m * t)
    return 0;
  return 1;
}
long long cb(long long l, long long r) {
  long long lt = l, rt = r;
  while (rt - lt > 1) {
    long long mid = (lt + rt) / 2;
    if (verify(mid))
      lt = mid;
    else
      rt = mid;
  }
  if (lt == l) return -1;
  return lt;
}
int main() {
  cin >> A >> B >> N;
  while (N--) {
    cin >> l >> t >> m;
    cout << cb(l - 1, t * m + 1) << '\n';
  }
  return 0;
}
