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 int A, B, l, t, m;
bool predicate(long long int val) {
  if (((A + (val - 1) * B <= t) &&
       ((A * (val - l + 1) +
         B * ((val * (val - 1)) / 2 - ((l - 1) * (l - 2)) / 2)) <= m * t)))
    return false;
  else
    return true;
}
int main() {
  long long int n, lw, hg, md;
  scanf("%lld", &A);
  scanf("%lld", &B);
  scanf("%lld", &n);
  while (n--) {
    scanf("%lld", &l);
    scanf("%lld", &t);
    scanf("%lld", &m);
    lw = l;
    hg = lw + m * t;
    while (lw < hg) {
      md = lw + (hg - lw + 1) / 2;
      if (predicate(md)) {
        hg = md - 1;
      } else {
        lw = md;
      }
    }
    if (predicate(lw)) {
      printf("-1\n");
    } else {
      printf("%lld\n", lw);
    }
  }
  return 0;
}
