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 int N = 1e6 + 2;
long long Wyszukaj(long long p, long long k, long long l, long long t,
                   long long m, long long A, long long B) {
  long long s, suma;
  bool czy;
  while (p < k) {
    s = (p + k + 1) / 2;
    suma = ((A + (l - 1) * B + A + (s - 1) * B) * (s - l + 1)) / 2;
    czy = true;
    if (A + (s - 1) * B > t) czy = false;
    if (suma > m * t) czy = false;
    if (czy)
      p = s;
    else
      k = s - 1;
  }
  if (p < l) return -1;
  return p;
}
int main() {
  long long A, B, l, t, m;
  int n, i;
  cin >> A >> B >> n;
  for (i = 0; i < n; i++) {
    cin >> l >> t >> m;
    cout << Wyszukaj(l - 1, l + N, l, t, m, A, B) << "\n";
  }
  return 0;
}
