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;
unsigned long long a, b;
unsigned long long getHeight(unsigned long long x) { return b * x + (a - b); }
unsigned long long getArea(unsigned long long h1, unsigned long long h2,
                           unsigned long long b) {
  return (h1 + h2) * b / 2;
}
int main() {
  unsigned long long n, m, t, l, r, midX, midY, startX, startY, maxArea;
  cin >> a >> b >> n;
  for (int i = 0; i < n; i++) {
    cin >> l >> t >> m;
    maxArea = r = m * t;
    startX = l;
    startY = getHeight(startX);
    if (startY > t) {
      cout << -1 << endl;
    } else {
      while (l < r) {
        midX = (l + r + 1) / 2;
        midY = getHeight(midX);
        if (midY <= t && getArea(startY, midY, midX - startX + 1) <= maxArea)
          l = midX;
        else
          r = midX - 1;
      }
      cout << r << endl;
    }
  }
  return 0;
}
