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;
const double EPS = 1E-12;
const long long mod = 1000000007;
using namespace std;
long long n, a, b, l, t, m;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> a >> b >> n;
  for (int i = 0; i < n; i++) {
    cin >> l >> t >> m;
    if (a + b * (l - 1) > t) {
      cout << -1 << endl;
      continue;
    }
    l--;
    long long rl = l;
    long long k = (t - a) / b;
    long long rr = k;
    long long mid, sm;
    while (rr - rl > 1) {
      mid = (rr + rl) / 2;
      sm = (mid - l + 1) * (a + b * l) + b * ((mid - l) * (mid - l + 1) / 2);
      if (sm <= t * m) {
        rl = mid;
      } else {
        rr = mid;
      }
    }
    mid = rr;
    sm = (mid - l + 1) * (a + b * l) + b * ((mid - l) * (mid - l + 1) / 2);
    if (sm <= t * m)
      mid = rr;
    else
      mid = rl;
    cout << mid + 1 << endl;
  }
  return 0;
}
