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
/**  _ _
 * \(^.^\)
 *  ( 8 ;)
 *  ( __;)
 *   V  V
 * by Abril
 */

import java.io.*;
import java.util.*;

public class Main {
	
	final int N = (int)1e6 + 1000;
	
	void solve() {
		long A = in.nextInt();
		long B = in.nextInt();
		int qq = in.nextInt();
		long[] sum = new long[N];
		sum[0] = 0;
		for (int i = 1; i < N; i++) {
			sum[i] = sum[i - 1] + A + B * (i - 1);
		}
		while (qq-- != 0) {
			int l = in.nextInt();
			int t = in.nextInt();
			int m = in.nextInt();
			int izq = l - 1, der = N;
			while (der - izq > 1) {
				int med = (der + izq) / 2;
				if (Math.max(A + B * (med - 1), (sum[med] - sum[l - 1] + m - 1) / m) <= t) {
					izq = med;
				} else {
					der = med;
				}
			}
			if (izq < l) izq = -1;
			out.println(izq);
		}
	}
	
	void run() {
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}
	
	InputReader in;
	PrintWriter out;
	
	class InputReader {
		BufferedReader br;
		StringTokenizer st;
		
		InputReader(InputStream is) {
			br = new BufferedReader(new InputStreamReader(is));
			st = null;
		}
		
		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}
}