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.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
	static BufferedReader reader;
	static StringTokenizer tokenizer;
	static PrintWriter writer;

	static int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	static long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	static double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	static boolean eof = false;

	static String nextToken() throws IOException {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			tokenizer = new StringTokenizer(reader.readLine());
		}
		return tokenizer.nextToken();
	}

	public static void main(String[] args) throws IOException {
		tokenizer = null;
		// reader = new BufferedReader(new FileReader("grave.in"));
		// writer = new PrintWriter(new FileWriter("grave.out"));
		reader = new BufferedReader(new InputStreamReader(System.in, "ISO-8859-1"));
		writer = new PrintWriter(System.out);
		banana();
		reader.close();
		writer.close();
	}

	static boolean test(long l, long r, long t, long m, long a, long b) {
		if ((a + (r - 1) * b) > t)
			return false;

		long sum = (r - l + 1) * (2 * a + (l + r - 2) * b) / 2;

		if (sum > t * m)
			return false;

		return true;
	}

	static void banana() throws IOException {
		long a = nextLong();
		long b = nextLong();
		long n = nextLong();

		for (int i = 0; i < n; ++i) {
			long l = nextInt();
			long ll = l;
			long t = nextInt();
			long m = nextInt();

			if (a + (l - 1) * b > t) {
				writer.println(-1);
				continue;
			}

			long rr = 1000000;

			while (rr - ll > 1) {
				long mid = (rr + ll) / 2;

				if (test(l, mid, t, m, a, b))
					ll = mid;
				else
					rr = mid;
			}
			if (test(l, rr, t, m, a, b))
				writer.println(rr);
			else
				writer.println(ll);

		}
	}
}