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;
void imprimirVector(vector<int> v) {
  if (!v.empty()) {
    int p = v.size();
    cout << "[";
    for (int i = 0; i < (int)(p - 1); i++) cout << v[i] << ",";
    cout << v[p - 1] << "]" << endl;
  } else
    cout << "[]" << endl;
}
long long cuadratica(double a, double b, double c) {
  long long res = floor((-b + sqrt(b * b - 4 * a * c)) / (2 * a));
  return res;
}
int query(long long A, long long B, long long l, long long t, long long m) {
  if (t < (A + (l - 1) * B))
    return -1;
  else
    return min(cuadratica(B, (2 * A - B),
                          2 * (1 - l) * (A + B * l) - 2 * B + B * l * l +
                              B * l - 2 * m * t),
               (t - A + B) / B);
}
int main() {
  long long n, A, B;
  cin >> A >> B >> n;
  for (int i = 0; i < (int)(n); i++) {
    long long l, t, m;
    cin >> l >> t >> m;
    cout << query(A, B, l, t, m) << endl;
  }
  return 0;
}
