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.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long a = in.nextLong();
        long b = in.nextLong();
        int n = in.nextInt();
        for (int i = 0; i < n; ++i) {
            long l = in.nextLong();
            long t = in.nextLong();
            long m = in.nextLong();
            if (t < a + (l - 1) * b) {
                System.out.println(-1);
            } else {
                long right = (t - a) / b + 2;
                long left = l;
                while (right - left > 1) {
                    long middle = (left + right) / 2;
                    if (t * m >= (l - 1 + middle - 1) * (middle - l + 1) / 2 * b + (middle - l + 1) * a) {
                        left = middle;
                    } else {
                        right = middle;
                    }
                }
                System.out.println(left);
            }
        }
    }
}