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 int a, d;
vector<long long int> val(10000007, 0);
vector<long long int> su(10000007, 0);
int main() {
  long long int q, n, x, y, i, j, k, ans = 0, lim = 2000000;
  cin >> a >> d >> q;
  su[0] = val[0] = 0;
  for (i = 1; i <= 2000000; i++) {
    val[i] = a + (i - 1) * d;
    su[i] = su[i - 1] + val[i];
  }
  while (q--) {
    long long int l, t, m;
    cin >> l >> t >> m;
    if (a + (l - 1) * d > t) {
      cout << "-1\n";
      continue;
    }
    int ta, tb;
    ta = lower_bound(su.begin() + l, su.begin() + lim, t * m + su[l - 1]) -
         su.begin();
    tb = lower_bound(val.begin() + l, val.begin() + lim, t) - val.begin();
    if (su[ta] != t * m + su[l - 1]) ta--;
    if (val[tb] != t) tb--;
    ta = min(ta, tb);
    if (ta >= l)
      cout << ta << "\n";
    else
      cout << "-1\n";
  }
  return 0;
}
