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;
long long n;
int check(long long mid, long long l, long long t, long long m) {
  long long biggest = mid * B + A - B;
  if (biggest > t) return 1;
  long long cnt = mid - l + 1;
  long long smallest = l * B + A - B;
  long long sum = (biggest + smallest) * cnt / 2;
  if (t * min(m, cnt) < sum)
    return 1;
  else
    return 0;
}
long long calc(long long _l, long long t, long long m) {
  long long l = _l;
  long long r = 1 << 20;
  while (r - l > 1) {
    long long mid = (l + r) / 2;
    if (check(mid, _l, t, m))
      r = mid;
    else
      l = mid;
  }
  return (check(l, _l, t, m) == 0) ? l : -1;
}
int main() {
  long long l, t, m;
  cin >> A >> B >> n;
  for (int i = 0; i < n; ++i) {
    cin >> l >> t >> m;
    long long res = calc(l, t, m);
    cout << res << endl;
  }
  return 0;
}
