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 a, b, n, ll, t, m;
bool check(long long x) {
  long long mx = a + (x - 1) * b;
  if (mx > t) return false;
  long long mn = a + (ll - 1) * b;
  if (((mx + mn) * (x - ll + 1)) / 2 > m * t) return false;
  return true;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cin >> a >> b >> n;
  ll = 1, t = 5, m = 3;
  for (long long i = 0; i < n; i++) {
    cin >> ll >> t >> m;
    long long l = ll, r = 1e8;
    while (r - l > 3) {
      long long mid = (l + r) / 2;
      if (check(mid))
        l = mid;
      else
        r = mid - 1;
    }
    bool f = false;
    for (long long j = r; j >= l; j--) {
      if (check(j)) {
        cout << j << "\n";
        f = true;
        break;
      }
    }
    if (!f) cout << -1 << "\n";
  }
  return 0;
}
