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;
template <class T>
T abs(T x) {
  return x > 0 ? x : -x;
}
int n;
int m;
int a, b;
long long get(int l, int r, int m) {
  long long x = a + (long long)(l - 1) * b;
  long long y = a + (long long)(r - 1) * b;
  long long sum = (x + y) * (r - l + 1) / 2;
  return max((sum + m - 1) / m, y);
}
int main() {
  scanf("%d%d%d", &a, &b, &n);
  for (int i = 0; i < n; i++) {
    int x, t, m;
    scanf("%d%d%d", &x, &t, &m);
    if (get(x, x, m) > t)
      printf("-1\n");
    else {
      int l = x, r = x + 2e6;
      while (r - l > 1) {
        int s = (l + r) / 2;
        if (get(x, s, m) > t)
          r = s;
        else
          l = s;
      }
      printf("%d\n", l);
    }
  }
  return 0;
}
