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.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author PM
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
    long A, B;
    long turnsToConsume(long l, long r, long m) {
        long width = r-l+1;
        m = Math.min(m, width);
        long area = width * (A+B*l) + (width*(width-1))/2 * B;
        long res = Math.max((area + m - 1) / m, (A + r * B));
//        System.out.println("l="+l+ " r=" + r + " m=" + m + " area=" + area + " res=" + res);
        return res;
    }
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        A = in.nextLong();
        B = in.nextLong();
        int n = in.nextInt();

        //list l, t, m (--)
        for (int i = 0; i < n; i++) {
            long l = in.nextLong()-1;
            long t = in.nextLong();
            long m = in.nextLong();
            if (A + l * B > t) {    //impossible
                out.println(-1);
                continue;
            }
            //bin search
            long mxR = t+1;       //surely not enough to eat the highest
            long miR = l;
            long r = (mxR + miR)/2;
            while (mxR - miR > 1) {
                if (turnsToConsume(l,r,m)>t) {
                    mxR = r;
                } else miR = r;
                r = (mxR + miR)/2;
            }
            out.println(miR+1);
        }
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

}

