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;
int f(long long l, long long r, long long m, long long t) {
  if (A + B * (r - 1) > t) return 0;
  if ((A + B * (l - 1) + A + B * (r - 1)) * (r - l + 1) / 2 > m * t) return 0;
  return 1;
}
int main() {
  int n;
  int l, t, m;
  cin >> A >> B >> n;
  int i;
  int rl, rmid, rr;
  for (i = 0; i < n; ++i) {
    scanf("%d%d%d", &l, &t, &m);
    if (!f(l, l, m, t)) {
      printf("-1\n");
      continue;
    }
    rl = l;
    rr = t + 1;
    while (rr - rl > 1) {
      rmid = (rr + rl) / 2;
      if (f(l, rmid, m, t))
        rl = rmid;
      else
        rr = rmid;
    }
    printf("%d\n", rl);
  }
  return 0;
}
