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 <typename T>
inline string toString(T a) {
  ostringstream os("");
  os << a;
  return os.str();
}
template <typename T>
inline long long toLong(T a) {
  long long res;
  istringstream os(a);
  os >> res;
  return res;
}
template <typename T>
inline T SQ(T a) {
  return a * a;
}
template <typename T>
inline unsigned long long bigmod(T a, T b, T m) {
  if (b == 0)
    return 1;
  else if (b % 2 == 0)
    return SQ(bigmod(a, b / 2, m)) % m;
  else
    return (a % m * bigmod(a, b - 1, m)) % m;
}
template <typename T>
inline vector<string> parse(T str) {
  vector<string> res;
  string s;
  istringstream os(str);
  while (os >> s) res.push_back(s);
  return res;
}
template <typename T>
inline unsigned long long dist(T A, T B) {
  unsigned long long res =
      (A.x - B.x) * (A.x - B.x) + (A.y - B.y) * (A.y - B.y);
  return res;
}
template <typename T>
inline double cosAngle(T a, T b, T c) {
  double res = a * a + b * b - c * c;
  res = res / (2 * a * b);
  res = acos(res);
  return res;
}
long long cal(long long n) {
  if (n == 0) return 0;
  n--;
  return (n * (n + 1)) / 2LL;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie();
  long long A, B, N;
  long long t, l, m;
  cin >> A >> B >> N;
  for (int i = (1); i <= (N); i++) {
    cin >> l >> t >> m;
    long long low = l, high = (long long)l + m + 1;
    long long best = -1;
    high = 1000000000LL;
    while (low <= high) {
      long long mid = (low + high) / 2;
      long long sum = cal(mid) - cal(l - 1);
      sum *= B;
      sum += ((long long)(mid - l + 1) * A);
      long long a = sum / m;
      if (sum % m) a++;
      long long b = (mid - 1) * B + A;
      a = (a > b ? a : b);
      if (a <= t) {
        best = mid;
        low = mid + 1LL;
      } else {
        high = mid - 1LL;
      }
    }
    cout << best << endl;
  }
}
