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 a, b, n;
long long l, t, m;
long long low, high, s1, s2, mid;
bool judge(int mid, int s1, int s2) {
  if ((mid - l + 1) * (s1 + s2) / 2 <= t * m)
    return true;
  else
    return false;
}
void solve() {
  high = (t - a) / b + 1;
  low = l;
  while (low <= high) {
    mid = (high + low) / 2;
    s2 = a + (mid - 1) * b;
    if (judge(mid, s1, s2))
      low = mid + 1;
    else
      high = mid - 1;
  }
  printf("%lld\n", low - 1);
}
int main() {
  while (~scanf("%d%d%d", &a, &b, &n)) {
    while (n--) {
      scanf("%lld%lld%lld", &l, &t, &m);
      s1 = a + (l - 1) * b;
      if (s1 > t)
        printf("-1\n");
      else {
        solve();
      }
    }
  }
  return 0;
}
