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;
long long l, t, m;
long long ans = 0;
long long a, b, n;
long long tok(long long i) { return (i - 1) * b + a; }
long long top(long long ilk, long long son, long long f) {
  long long to = (ilk + son) * (son - ilk + f);
  to /= f;
  return to / 2;
}
int bs(int ll, int rr) {
  if (ans != 0) return 0;
  int mid = (ll + rr) / 2;
  if (ll == rr) {
    if (top(tok(l), tok(ll), b) <= t * m && tok(ll) <= t) ans = ll;
    return 0;
  }
  if (top(tok(l), tok(mid + 1), b) <= t * m && tok(mid + 1) <= t)
    bs(mid + 1, rr);
  else if (top(tok(l), tok(ll), b) <= t * m && tok(ll) <= t)
    bs(ll, mid);
  return 0;
}
int fun() {
  if (tok(l) > t) {
    cout << -1 << endl;
  } else {
    ans = 0;
    bs(l, 1000009);
    cout << ans << endl;
  }
  return 0;
}
int main() {
  cin >> a >> b >> n;
  while (n--) {
    cin >> l >> t >> m;
    fun();
  }
  return 0;
}
