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.IOException;
import java.util.Scanner;

public class LuckyNumber {
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        int a = sc.nextInt(); int b = sc.nextInt(); int n = sc.nextInt();
        for (int i = 0; i < n; ++i) {
            long l = sc.nextInt();
            long t = sc.nextInt();
            long m = sc.nextInt();
            long mx = (t - a) / b + 1;
            long lastSuccess = -1;
            long start = l;
            long max_num = m * t;
            boolean found = false;
            while (start <= mx) {
                long mid = (start + mx) / 2;
                long cur = hh(a, b, l, mid);
                if (cur > max_num) {
                    mx = mid - 1;
                } else if (cur < max_num) {
                    lastSuccess = mid;
                    start = mid + 1;
                } else {
                    System.out.println(mid);
                    found = true;
                    break;
                }
            }
            if (! found)
                System.out.println(lastSuccess);
        }
    }

    private static long hh(long a, long b, long l, long r) {
        return a * (r - l + 1) + b * (r * (r - 1) / 2 - (l - 1) * (l - 2) / 2);
    }
}
