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, l, t, m;
long long s(long long x) { return (a + b * (x - 1)); }
bool chk_sum(long long x, long long y) {
  long long sum =
      a * (y - x + 1) + b * ((y * (y - 1) / 2) - ((x - 1) * (x - 2) / 2));
  return (sum <= m * t);
}
int main() {
  cin >> a >> b >> n;
  while (n--) {
    cin >> l >> t >> m;
    if (t < s(l))
      cout << "-1" << endl;
    else {
      long long e = l, d = 10000000, med;
      while (e + 1 < d) {
        med = (e + d) / 2;
        if (s(med) <= t && chk_sum(l, med))
          e = med;
        else
          d = med;
      }
      cout << e << endl;
    }
  }
}
