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;
const int MAX = 2e5 + 3;
const long long MOD = 1e9 + 7;
long long A, B, n;
long long S(long long n, long long a, long long d) {
  return ((2LL * a + (n - 1) * d) * n) / 2;
}
long long term(long long i) { return A + (i - 1) * B; }
long long check(long long L, long long m, long long t, long long x) {
  if (t < term(L + x - 1)) return false;
  long long tot = S(x, term(L), B);
  long long lagbe = (tot / m) + (tot % m > 0);
  return lagbe <= t;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> A >> B >> n;
  while (n--) {
    long long l, t, m;
    cin >> l >> t >> m;
    if (!check(l, m, t, 1)) {
      cout << "-1\n";
      continue;
    }
    long long lo = 1, hi = 1e6;
    while (hi > lo) {
      long long mid = (lo + hi + 1) / 2;
      if (check(l, m, t, mid))
        lo = mid;
      else
        hi = mid - 1;
    }
    cout << l + lo - 1 << "\n";
  }
}
