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;
inline bool checkBit(long long n, int i) { return n & (1LL << i); }
inline long long setBit(long long n, int i) {
  return n | (1LL << i);
  ;
}
inline long long resetBit(long long n, int i) { return n & (~(1LL << i)); }
int dx[] = {0, 0, +1, -1};
int dy[] = {+1, -1, 0, 0};
inline bool EQ(double a, double b) { return fabs(a - b) < 1e-9; }
long long A, B, l, t, m;
int n;
long long summation(long long num, long long start) {
  long long ret = 2 * start + (num - 1);
  ret *= num;
  return ret / 2;
}
bool valid(long long val) {
  int num = val - l + 1;
  if (t < A + (val - 1) * B) return false;
  long long sum = (num) * (A - B) + (B * (summation(num, l)));
  return sum <= (t * m);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> A >> B >> n;
  while (n--) {
    cin >> l >> t >> m;
    long long low = l, high = (long long)1e13;
    ;
    if (!valid(low)) {
      cout << -1 << '\n';
      continue;
    }
    while (low < high) {
      long long mid = (low + high + 1) / 2;
      if (valid(mid))
        low = mid;
      else
        high = mid - 1;
    }
    cout << low << '\n';
  }
  return 0;
}
