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 long long maxn = 1e5 + 500;
long long a, b;
long long f(long long n) { return a + (n - 1) * b; }
bool good(long long l, long long r, long long m, long long t) {
  long long ans = f(r);
  long long tol = (r - l + 1);
  long long par = (tol) * (f(l)) + b * (tol * (tol - 1) / 2);
  if (t < ans) return 0;
  if (t * m < par) return 0;
  return 1;
}
int main() {
  long long n;
  cin >> a >> b >> n;
  for (long long i = 0; i < n; i++) {
    long long l, t, m;
    cin >> l >> t >> m;
    if (!good(l, l, m, t)) {
      cout << -1;
    } else {
      long long s = l, e = 1e12;
      while (e - s > 1) {
        long long mm = (s + e) / 2;
        if (good(l, mm, m, t)) {
          s = mm;
        } else {
          e = mm;
        }
      }
      cout << s;
    }
    cout << endl;
  }
}
