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, n;
long long getTime(long long l, long long r, long long m) {
  long long val1 = (r - l + 1) * (A + B * (l - 1));
  val1 += B * ((r - l + 1) * (r - l)) / 2;
  long long d = m;
  long long ans = (val1 + d - 1) / d;
  if (A + (r - 1) * B > ans) ans = A + (r - 1) * B;
  return ans;
}
int main() {
  scanf("%d%d%d", &A, &B, &n);
  for (int i = (0); i < int(n); ++i) {
    int l, t, m;
    scanf("%d%d%d", &l, &t, &m);
    long long lo = l - 1, hi = l + 1000000;
    while (hi - lo > 1) {
      long long mid = (hi + lo) / 2;
      if (getTime(l, mid, m) > t)
        hi = mid;
      else
        lo = mid;
    }
    if (lo >= l)
      printf("%I64d\n", lo);
    else
      puts("-1");
  }
}
