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 taskA {

	void solve() throws IOException {
		long a = nextInt();
		long b = nextInt();
		int n = nextInt();
		for (int i = 0; i < n; i++) {
			long x = nextInt() - 1;
			long t = nextLong();
			long m = nextLong();
			long l = x;
			long r = x + t * 2;
			while (l < r - 1) {
				long c = (l + r) / 2;
				long len = c - x + 1;
				long cm = Math.min(m, len);
				if (a + b * c <= t
						&& cm * t >= len * a + len * (b * x) + len * (len - 1)
								/ 2 * b)
					l = c;
				else
					r = c;
			}
			long len = l - x + 1;
			long cm = Math.min(m, len);
			if (a + b * l <= t
					&& cm * t >= len * a + len * (b * x) + len * (len - 1) / 2
							* b)
				out.println(l + 1);
			else
				out.println(-1);

		}
	}

	BufferedReader br;
	StringTokenizer st;
	PrintWriter out;

	void run() {
		try {
			br = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			// br = new BufferedReader(new FileReader(new File("taskA.in")));
			// out = new PrintWriter("taskA.out");

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	public static void main(String[] args) {
		new taskA().run();
	}

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

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

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

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