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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;

@SuppressWarnings("javadoc")
public class TavasAndKarafs {

	public TavasAndKarafs() throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(
				System.out));

		String[] split = br.readLine().split(" ");

		long A = Long.parseLong(split[0]);
		long B = Long.parseLong(split[1]);
		int n = Integer.parseInt(split[2]);

		long l, t, m;

		for (int i = 0; i < n; i++) {
			split = br.readLine().split(" ");

			l = Long.parseLong(split[0]);
			t = Long.parseLong(split[1]);
			m = Long.parseLong(split[2]);

			if (A + (l - 1) * B > t) {
				bw.write("-1\n");
			} else {
				double sqrt = Math.sqrt((2 * A - B) * (2 * A - B) + 4 * B
						* (2 * A * l - 2 * A + B * (l - 1) * (l - 2) + 2 * m * t));
				double r1 = (B - 2d * A + sqrt) / (2d * B);
				long r2 = 1 + (t - A) / B;
				long r = (long) Math.min(r1, r2);
				if (r < l) {
					bw.write("-1\n");
				} else {
					bw.write(r + "\n");
				}
			}
		}
		br.close();
		bw.close();
	}

	public static void main(String[] args) throws IOException {
		new TavasAndKarafs();

	}

}
