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;
template <class X, class Y>
void amax(X& x, const Y& y) {
  if (x < y) x = y;
}
template <class X, class Y>
void amin(X& x, const Y& y) {
  if (x > y) x = y;
}
const int INF = 1e9 + 10;
const long long INFL = (long long)1e18 + 10;
int A, B, n;
bool check(int l, int r, int t, int m) {
  if ((long long)(r - 1) * B + A > t) return false;
  int len = r - l + 1;
  long long sum = (long long)A * len + (long long)(l - 1) * len * B;
  sum += (long long)(len - 1) * len / 2 * B;
  return sum <= (long long)t * m;
}
int bfind(int x, int t, int m) {
  int l = x, r = 1e7, i = (l + r) / 2;
  while (l != i && i != r) {
    if (check(x, i, t, m))
      l = i;
    else
      r = i;
    i = (l + r) / 2;
  }
  for (int i = r; i >= l; i--)
    if (check(x, i, t, m)) return i;
  return -1;
}
void process() {
  cin >> A >> B >> n;
  while (n--) {
    int l, t, m;
    cin >> l >> t >> m;
    cout << bfind(l, t, m) << '\n';
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  process();
}
