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>
#pragma comment(linker, "/STACK:268435456")
using namespace std;
const double PI = 3.1415926535897932384626433832795;
template <class T>
T min(T &a, T &b) {
  return (a < b) ? a : b;
}
template <class T>
T max(T &a, T &b) {
  return (a > b) ? a : b;
}
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
T abs(T &a) {
  return (a < 0) ? (-a) : a;
}
inline void read(int &x) { scanf("%d", &x); }
inline void readln(int &x) { scanf("%d\n", &x); }
inline void write(int x) { printf("%d", x); }
inline void writeln(int x) { printf("%d\n", x); }
inline void read(long long &x) { scanf("%lld", &x); }
inline void readln(long long &x) { scanf("%lld\n", &x); }
inline void write(long long x) { printf("%lld", x); }
inline void writeln(long long x) { printf("%lld\n", x); }
inline void read(double &x) { scanf("%lf", &x); }
inline void readln(double &x) { scanf("%lf\n", &x); }
inline void write(double x) { printf("%.15lf", x); }
inline void writeln(double x) { printf("%.15lf\n", x); }
inline void read(char *s) { scanf("%s", s); }
inline void readln(char *s) { scanf("%s\n", s); }
inline void write(char *s) { printf("%s", s); }
inline void writeln(char *s) { printf("%s\n", s); }
inline int readInt() {
  int x;
  read(x);
  return x;
}
inline long long readLong() {
  long long x;
  read(x);
  return x;
}
inline double readDouble() {
  double x;
  read(x);
  return x;
}
inline void showTime() {}
long long a, b, n;
long long l, t, m;
bool good(long long r) {
  long long xl = a + b * (l - 1);
  long long xr = a + b * (r - 1);
  long long sum = (xl + xr) * (r - l + 1) / 2;
  long long maxdoze = sum / m;
  long long result;
  if (xr > maxdoze)
    result = xr;
  else
    result = sum / m + ((sum % m) ? 1 : 0);
  return result <= t;
}
int main() {
  srand((unsigned)time(NULL));
  cin >> a >> b >> n;
  for (int i = 0; i < n; i++) {
    cin >> l >> t >> m;
    long long cur = l;
    long long step = 1 << 30;
    while (step) {
      if (good(cur + step)) {
        cur += step;
      }
      step >>= 1;
    }
    if (good(cur)) {
      cout << cur;
    } else {
      cout << -1;
    }
    cout << endl;
  }
  return 0;
}
