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 q, a, b, l, t, m;
long long yap() {
  long long bas = l;
  long long son = t + 2;
  long long alt = a + b * (l - 1);
  while (son - bas > 1) {
    long long uz = ((bas + son) / 2) - l;
    long long alan = (uz * (uz + 1) / 2) * b + uz * alt + alt;
    if (alan <= m * t and a + b * (((bas + son) / 2) - 1) <= t)
      bas = ((bas + son) / 2);
    else
      son = ((bas + son) / 2) - 1;
  }
  if (son - bas == 1) {
    long long uz = son - l;
    long long alan = (uz * (uz + 1) / 2) * b + uz * alt + alt;
    if (alan <= m * t and a + b * (son - 1) <= t)
      bas = son;
    else
      son = bas;
  }
  if (a + (((bas + son) / 2) - 1) * b > t) return -1;
  return ((bas + son) / 2);
}
int main() {
  scanf("%lld %lld %lld", &a, &b, &q);
  while (q--) {
    scanf("%lld %lld %lld", &l, &t, &m);
    printf("%lld\n", yap());
  }
  return 0;
}
