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
import java.util.Scanner;

public class TavasKafas {
  public static void main(String[] agrs) {
    Scanner in = new Scanner(System.in);
    int a = in.nextInt();
    int b = in.nextInt();
    int n = in.nextInt();
    for (int i = 0; i < n; i++) {
      int l = in.nextInt();
      int t = in.nextInt();
      int m = in.nextInt();
      long lo = l;
      long hi = (t + b - a) / b;
      if (hi < lo) System.out.println(-1);
      else {
        while (lo + 1 < hi) {
          long mid = (lo + hi) / 2;
          if (check(l, mid, a, b, t, m)) lo = mid;
          else hi = mid - 1;
        }
        if (check(l, hi, a, b, t, m)) System.out.println(hi);
        else System.out.println(lo);
      }
    }
  }
  
  public static boolean check(int l, long r, int a, int b, int t, int m) {
    long sigma = (r - l + 1) * a + (l + r - 2) * (r - l + 1) * b / 2;
    long min;
    if (sigma % m == 0) min = sigma / (long) m;
    else min = sigma / m + 1;
    if (min <= t) return true;
    else return false;
  }
}