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;
const long long mod = 1000000007LL;
int n;
long long a, b, l, t, m;
bool check(long long l, long long r, long long a, long long b, long long t,
           long long m) {
  long long d1 = r - l + 1;
  if (a + (r - 1) * b > t) {
    return false;
  }
  long long d2 = 2LL * a + (l + r - 2) * b;
  if (2LL * m * t / d1 >= d2) {
    return true;
  }
  return false;
}
int main() {
  cin >> a >> b >> n;
  for (int i = 1; i <= n; ++i) {
    scanf("%lld%lld%lld", &l, &t, &m);
    long long x = l, y = l + 1e12;
    while (x < y) {
      long long r = (x + y + 1) / 2;
      if (check(l, r, a, b, t, m)) {
        x = r;
      } else {
        y = r - 1;
      }
    }
    if (check(l, x, a, b, t, m)) {
      cout << x << endl;
    } else {
      cout << -1 << endl;
    }
  }
  return 0;
}
