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;
const long long INF = 1000000000000;
long long A, B, n, l, t, m, r;
bool check(long long len) {
  long long sum = A + (B * (l - 1));
  long long mx = A + (B * (len - 1));
  if (mx <= t && mx + sum <= 2 * m * t / (len - l + 1))
    return true;
  else
    return false;
}
long long BS(long long L, long long R) {
  if (L > R) return r;
  long long mid = L + R >> 1;
  if (check(mid)) {
    r = mid;
    return BS(mid + 1, R);
  } else
    return BS(L, mid - 1);
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> A >> B >> n;
  while (n--) {
    cin >> l >> t >> m;
    r = l - 1;
    BS(l, INF);
    if (r >= l)
      cout << r << '\n';
    else
      cout << -1 << '\n';
  }
}
