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>
int main() {
  int a, b, n;
  scanf("%d%d%d", &a, &b, &n);
  while (n--) {
    int l, t, m;
    int min, max, mid;
    scanf("%d%d%d", &l, &t, &m);
    if (a + 1LL * (l - 1) * b > t) {
      puts("-1");
      continue;
    }
    min = l;
    max = 1e7;
    while (min < max) {
      mid = (min + max + 1) / 2;
      if (1LL * std::min(mid - l + 1, m) * t >=
              (a + 1LL * (l - 1) * b + a + 1LL * (mid - 1) * b) *
                  (mid - l + 1) / 2 &&
          a + 1LL * (mid - 1) * b <= t)
        min = mid;
      else
        max = mid - 1;
    }
    printf("%d\n", min);
  }
}
