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 MOD = 1e9 + 7;
long long MAX = 1e17;
long long a, b, n;
long long m, t;
long long check(long long l, long long x) {
  long long ans = (x - l + 1) * a + b * (l - 1) * (x - l + 1) +
                  (b * (x - l) * (x - l + 1)) / 2;
  if (a + (x - 1) * b > t) return m * t + 1;
  return ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  ;
  cin >> a >> b >> n;
  while (n--) {
    long long L;
    cin >> L >> t >> m;
    long long l = L, r = L + m * t;
    while (r - l > 1) {
      long long mid = (l + r) / 2;
      if (check(L, mid) <= (min(m, mid - L + 1)) * t)
        l = mid;
      else
        r = mid;
    }
    if (check(L, r) > (min(m, r - L + 1)) * t) r = l;
    if (check(L, l) > (min(m, l - L + 1)) * t) r = -1;
    cout << r << endl;
  }
}
