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 int t, m, a, b, l;
long long int nc2(long long int k) { return k * (k - 1) / 2; }
bool check(long long int k) {
  long long int second = a * (k - l + 1) + b * (nc2(k) - nc2(l - 1));
  return second <= m * t && (a + (k - 1) * b <= t);
}
int main() {
  long long int n;
  scanf("%lld%lld", &a, &b), scanf("%lld", &n);
  while (n--) {
    scanf("%lld%lld", &l, &t), scanf("%lld", &m);
    long long int lo = l, hi = m * t + l + 1;
    if (!check(l)) {
      printf("%d\n", -1);
      continue;
    }
    while (lo < hi) {
      long long int mid = (lo + hi) >> 1;
      if (check(mid))
        lo = mid + 1;
      else
        hi = mid;
    }
    printf("%lld\n", lo - 1);
  }
  return 0;
}
