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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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 {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        long a = in.nextLong();
        long b = in.nextLong();
        long n = in.nextLong();

        for (int i = 0; i < n; i++) {
            long left = in.nextLong();
            long t = in.nextLong();
            long m = in.nextLong();

            out.println(solve(a, b, left, t, m));
        }
    }

    private long solve(long a, long b, long left, long t, long m) {
        long curr = a + (left - 1) * b;

        if (t < curr) {
            return -1;
        }

        long originalLeft = left;
        long right = left + t * m + 1;

        while (left <= right) {
            long mid = left + (right - left) / 2;
            long val = getVal(a, b, originalLeft, mid);

            if (val <= t * m && (a + (mid - 1) * b <= t)) {
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }

        return right;
    }

    private long getVal(long a, long b, long left, long right) {
        long n = right - left + 1;

        long first = a + (left - 1) * b;
        long last = a + (right - 1) * b;

        long t1 = n;
        long t2 = first + last;

        if (t1 % 2 == 0) {
            t1 = t1 / 2;
        } else {
            t2 = t2 / 2;
        }

        return t1*t2;
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;


    public InputReader(InputStream stream){
        reader = new BufferedReader(new InputStreamReader(stream));
    }

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

        return tokenizer.nextToken();
    }

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

