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;
namespace Solve {
template <class T>
inline bool _min(T& data, const T& comp) {
  if (comp < data) {
    comp = data;
    return true;
  }
  return false;
}
template <class T>
inline bool _max(T& data, const T& comp) {
  if (data < comp) {
    comp = data;
    return true;
  }
  return false;
}
template <class T>
inline vector<T>& operator<<(vector<T>& storage, const T& data) {
  storage.push_back(data);
  return storage;
}
template <class T>
inline void operator!(const vector<T>& vect) {
  for (const T& data : vect) {
    cout << data << " ";
  }
}
template <class T>
inline queue<T>& operator<<(queue<T>& storage, const T& data) {
  storage.push(data);
  return storage;
}
template <class T>
inline stack<T>& operator<<(stack<T>& storage, const T& data) {
  storage.push(data);
  return storage;
}
template <class T>
inline priority_queue<T>& operator<<(priority_queue<T>& storage,
                                     const T& data) {
  storage.push(data);
  return storage;
}
template <class T>
inline queue<T>& operator>>(queue<T>& storage, T& data) {
  data = storage.front();
  storage.pop();
  return storage;
}
template <class T>
inline stack<T>& operator>>(stack<T>& storage, T& data) {
  data = storage.top();
  storage.pop();
  return storage;
}
template <class T>
inline priority_queue<T>& operator>>(priority_queue<T>& storage, T& data) {
  data = storage.top();
  storage.pop();
  return storage;
}
long long A, B, n;
inline long long sum(const long long& l, const long long& r,
                     const long long& c) {
  return ((l + r) * c) >> 1;
}
inline long long height(const long long& p) { return A + B * (p - 1); }
inline bool OK(const long long& l, const long long& t, const long long& m,
               const long long& r) {
  long long R = height(r);
  long long tot = t * m;
  if (R > t) return false;
  if (sum(height(l), height(r), r - l + 1) > tot) return false;
  return true;
}
const long long RLIM = 10000000;
void main(void) {
  ios::sync_with_stdio(false);
  register int i, j;
  cin >> A >> B >> n;
  for (i = 0; i < n; ++i) {
    long long l, t, m;
    cin >> l >> t >> m;
    long long L = l, R = RLIM;
    while (L < R - 1) {
      long long mid = (L + R) >> 1;
      if (OK(l, t, m, mid))
        L = mid;
      else
        R = mid - 1;
    }
    if (OK(l, t, m, R)) L = R;
    cout << (OK(l, t, m, L) ? L : -1) << endl;
  }
}
}  // namespace Solve
int main(void) { Solve::main(); }
