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 mod = 1e9 + 7;
bool check(long long mid, long long t, long long m, long long l, long long a,
           long long b) {
  long long aa = a * (mid - l + 1) +
                 b * ((mid * (mid - 1) / 2) - (((l - 1) * (l - 2))) / 2);
  return aa <= t * m;
}
void solve() {
  long long a, b, n;
  cin >> a >> b >> n;
  while (n--) {
    long long l, t, m;
    cin >> l >> t >> m;
    if (a + (l - 1) * b > t)
      cout << -1 << "\n";
    else {
      long long tt = l;
      long long r = (t - a) / b + 2;
      while (l + 1 < r) {
        long long mid = (l + r) / 2;
        if (check(mid, t, m, tt, a, b))
          l = mid;
        else
          r = mid;
      }
      cout << l << "\n";
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  long long no_of_test_cases = 1;
  while (no_of_test_cases--) {
    solve();
  }
  return 0;
}
