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 CF535C {
	static long solve(long a, long b, long t, long m) {
		if (a > t)
			return 0;
		long lower = 1;
		long upper = t * m / a + 1;
		while (upper - lower > 1) {
			long k = (lower + upper) / 2;
			long c = a + (k - 1) * b;
			if (c <= t && k * (a + c) / 2 <= m * t)
				lower = k;
			else
				upper = k;
		}
		return lower;
	}
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		long a = Long.parseLong(st.nextToken());
		long b = Long.parseLong(st.nextToken());
		long n = Long.parseLong(st.nextToken());
		for (int i = 0; i < n; i++) {
			st = new StringTokenizer(br.readLine());
			long l = Long.parseLong(st.nextToken());
			long t = Long.parseLong(st.nextToken());
			long m = Long.parseLong(st.nextToken());
			long k = solve(a + (l - 1) * b, b, t, m);
			pw.println(k == 0 ? -1 : l + k - 1);
		}
		pw.close();
	}
}
