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
//package codeforces.cfr299div2;

import java.util.Scanner;

/**
 * Created by bistrashkin on 4/14/15.
 */
public class C {
    private static boolean canEat(long A, long B, long l, long m, long t, long r) {
        long count = r - l + 1;
        long first = A + B * (l - 1);
        long last = A + B * (r - 1);
        return last <= t && ((first + last) * count) / 2 <= m * t;
    }

    private static long binarySearch(long A, long B, long l, long m, long t) {
        long maxR = (t - A) / B + 1;
        long minR = l;
        if (!canEat(A, B, l, m, t, minR)) {
            return -1;
        }
        while (maxR - minR > 1) {
            long midR = (minR + maxR) / 2;
            if (canEat(A, B, l, m, t, midR)) {
                minR = midR;
            } else {
                maxR = midR - 1;
            }
        }
        return canEat(A, B, l, m, t, maxR) ? maxR : minR;
    }

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long A = in.nextLong();
        long B = in.nextLong();
        long n = in.nextLong();
        for (long i = 0; i < n; i++) {
            long l = in.nextLong();
            long t = in.nextLong();
            long m = in.nextLong();
            System.out.println(binarySearch(A, B, l, m, t));
        }
    }
}
