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;
long long n, A, B, l, t, m, ans;
long long find(long long s, long long e) {
  if (s == e) return s;
  long long x = (s + e) / 2 + 1;
  if ((2 * A + (l + x - 2) * B) * (x - l + 1) > 2 * m * t ||
      A + (x - 1) * B > t)
    return find(s, x - 1);
  else
    return find(x, e);
}
int main() {
  scanf("%I64d%I64d%I64d", &A, &B, &n);
  for (int i = 0; i < n; i++) {
    scanf("%I64d%I64d%I64d", &l, &t, &m);
    if (A + (l - 1) * B > t)
      ans = -1;
    else
      ans = find(l, l + m * t);
    printf("%I64d\n", ans);
  }
  return 0;
}
