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

public class Main {

	BufferedReader in;
	StringTokenizer str = null;
	PrintWriter out;
	
	private String next() throws Exception{
		while (str == null || !str.hasMoreElements())
			str = new StringTokenizer(in.readLine());
		return str.nextToken();
	}
	
	private int nextInt() throws Exception{
		return Integer.parseInt(next());
	}
	
	private long nextLong() throws Exception{
		return Long.parseLong(next());
	}
	
	private double nextDouble() throws Exception{
		return Double.parseDouble(next());
	}

	long a, b;
	
	public void run() throws Exception{
		in =  new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		a = nextInt();
		b = nextInt();
		int Q = nextInt();
		while(Q-->0) {
			int l = nextInt(), t = nextInt(), m = nextInt();
			long lo = l - 1, hi = 100000000000L;
			while(hi - lo > 1) {
				long mid = lo + (hi - lo) / 2;
				if (can(l, mid, m, t)) {
					lo = mid;
				}else {
					hi = mid;
				}
			}
			if (lo == l - 1) {
				out.println(-1);
			}else {
				out.println(lo);
			}
		}
		out.close();
	}

	private boolean can(long l, long r, long m, int t) {
		long h = a + b * (r - 1);
		if (h > t) return false;
		long s = (2 * a + b * (l + r - 2));
		if (s % 2 == 0) {
			s /= 2;
			s *= (r - l + 1);
		}else {
			s *= (r - l + 1) / 2;
		}
		return s <= m * t;
	}
		
	public static void main(String[] args) throws Exception{
		new Main().run();
	}
}
