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;
int INT_MAX_VAL = (int)1e20;
int INT_MIN_VAL = (int)-1e20;
long long LONG_MAX_VAL = (long long)1e20;
long long LONG_MIN_VAL = (long long)-1e20;
long long a, b, n;
long long func(long long l, long long r, long long m, long long t) {
  if (a + (r - 1) * b > t) return false;
  long long d = r - l + 1;
  long long prod = a * d + b * (r + l - 2) * d / 2;
  return prod <= (t * m);
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cin >> a >> b >> n;
  for (long long(T) = 0LL; (T) < (n); (T)++) {
    long long l, t, m;
    cin >> l >> t >> m;
    long long cur = a + (l - 1) * b;
    if (cur > t) {
      cout << "-1" << '\n';
      continue;
    }
    long long lt = l;
    long long rt = 100000000;
    while (lt < rt) {
      long long med = (rt + lt + 1) / 2;
      if (func(l, med, m, t)) {
        lt = med;
      } else {
        rt = med - 1;
      }
    }
    cout << rt << '\n';
  }
  return 0;
}
