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 N = 1e5 + 5;
long long a, b, n;
long long l, t, m;
bool check(long long x) {
  long long reqd = 0;
  long long mx = a + (x - 1) * b;
  if (mx > t) return 0;
  long long sum = (x - l + 1) * a;
  long long other = (x * (x - 1) / 2) - (l - 1) * (l - 2) / 2;
  double temp = other;
  temp *= b;
  temp += sum;
  if (temp / m > t) return 0;
  sum += other * b;
  return ((sum + m - 1) / m <= t);
}
long long binsearch(long long lo, long long hi) {
  while (lo < hi) {
    long long mid = (lo + hi + 1) / 2;
    if (check(mid))
      lo = mid;
    else
      hi = mid - 1;
  }
  if (!check(lo)) return -1;
  return lo;
}
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  cin >> a >> b >> n;
  while (n--) {
    cin >> l >> t >> m;
    long long ans = binsearch(l, 1e9);
    cout << ans << "\n";
  }
  return 0;
}
