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.math.BigInteger;
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 shu_mj @ http://shu-mj.com
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskA solver = new TaskA();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskA {
    Scanner in;
    PrintWriter out;

    public void solve(int testNumber, Scanner in, PrintWriter out) {
        this.in = in;
        this.out = out;
        run();
    }

    void run() {
        int a = in.nextInt();
        int b = in.nextInt();
        int n = in.nextInt();
        while (n-- != 0) {
            int l = in.nextInt();
            int t = in.nextInt();
            int m = in.nextInt();
            int L = 0, R = (int) (2e6);
            while (L < R) {
                int M = (L + R) / 2;
                if (fit(a, b, l, M, t, m)) L = M + 1;
                else R = M;
            }
            out.println(L == 0 ? -1 : l + L - 1);
        }
    }

    private boolean fit(int a, int b, int l, int r, int t, int m) {
        long sum = (long) a * (r + 1) + (long) b * (l - 1 + l + r - 1) * (r + 1) / 2;
        long max = a + (long) b * (l + r - 1);
//        Algo.debug(a, b, l, r, t, m, sum, max);
        return max <= t && sum <= (long) m * t;
    }
}

class Scanner {
    BufferedReader br;
    StringTokenizer st;

    public Scanner(InputStream in) {
        br = new BufferedReader(new InputStreamReader(in));
        eat("");
    }

    private void eat(String s) {
        st = new StringTokenizer(s);
    }

    public String nextLine() {
        try {
            return br.readLine();
        } catch (IOException e) {
            return null;
        }
    }

    public boolean hasNext() {
        while (!st.hasMoreTokens()) {
            String s = nextLine();
            if (s == null)
                return false;
            eat(s);
        }
        return true;
    }

    public String next() {
        hasNext();
        return st.nextToken();
    }

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

}

