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.

<image>

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;
bool flag(int r) {
  long long ar, al, sum;
  ar = a + (r - 1) * b;
  if (ar > t) return false;
  al = a + (l - 1) * b;
  sum = (al + ar) * (r - l + 1) / 2;
  if (sum > t * m) return false;
  return true;
}
long long solve() {
  long long x = l, y = (t - a) / b + 1;
  while (x < y) {
    long long mid = (x + y) >> 1;
    if (flag(mid))
      x = mid + 1;
    else
      y = mid - 1;
  }
  if (!flag(x)) x--;
  return x;
}
int main() {
  scanf("%I64d%I64d%I64d", &a, &b, &n);
  while (n--) {
    scanf("%I64d%I64d%I64d", &l, &t, &m);
    long long val_l = a + (l - 1) * b;
    if (val_l > t)
      puts("-1");
    else {
      long long r = solve();
      printf("%I64d\n", r);
    }
  }
  return 0;
}
