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, t, m, l;
bool ok(int r) {
  long long sum, sl, rest, sr, impart;
  sl = A + (1ll * l - 1) * 1ll * B;
  sr = A + (1ll * r - 1) * 1ll * B;
  impart = min(m, (r - l + 1));
  if (sr > t) return 0;
  sum = (sl + sr) * (r - l + 1) / 2;
  rest = sum % m;
  sum = sum / m;
  if (rest) sum++;
  if (sum <= t) return 1;
  return 0;
}
int binarySearch(int st, int dr) {
  int med, last = -1;
  while (st <= dr) {
    med = (1ll * st + dr) / 2;
    if (ok(med)) {
      last = med;
      st = med + 1;
    } else
      dr = med - 1;
  }
  return last;
}
int main() {
  int n, i, k;
  scanf("%d%d%d", &A, &B, &n);
  for (i = 1; i <= n; i++) {
    scanf("%d%d%d", &l, &t, &m);
    k = binarySearch(l, 2000000000);
    printf("%d\n", k);
  }
  return 0;
}
