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;
int a, b, n;
int l, t, m;
bool check(int n) {
  if (a + 1LL * (l + n - 1) * b > t) return false;
  long long val = a + 1LL * (l - 1) * b;
  long long tc = 1LL * t * m - val * (n + 1);
  if (tc < 0) return false;
  tc = tc - 1LL * n * (n + 1) / 2 * b;
  return tc >= 0;
}
int main() {
  scanf("%d%d%d", &a, &b, &n);
  for (int i = 0; i < n; ++i) {
    scanf("%d%d%d", &l, &t, &m);
    long long r = a + 1LL * (l - 1) * b;
    if (r > t) {
      printf("-1\n");
      continue;
    }
    int lm = 0, rm = 2000000;
    while (lm + 1 < rm) {
      int cm = (lm + rm) / 2;
      if (check(cm))
        lm = cm;
      else
        rm = cm;
    }
    cout << lm + l << endl;
  }
  return 0;
}
