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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mthai
 */
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);
        CF_535C solver = new CF_535C();
        solver.solve(1, in, out);
        out.close();
    }

    static class CF_535C {
        public void solve(int testNumber, Scanner input, PrintWriter out) {
            ShortScanner in = new ShortScanner(input);
            int a = in.i(), b = in.i(), n = in.i();
            int len = 1000001;
            long[] s = new long[len], sum = new long[len];
            for (int i = 0; i < len; ++i) {
                s[i] = 1l * a + 1l * i * b;
                sum[i] = (i > 0) ? sum[i - 1] + s[i] : s[i];
            }
            while (n-- > 0) {
                int l = in.i() - 1, t = in.i(), m = in.i();
                int low = l, hi = len - 1, ans = -1;
                while (low <= hi) {
                    int mid = low + (hi - low) / 2;
                    long dif = (l == 0) ? sum[mid] : sum[mid] - sum[l - 1];
                    if (dif - 1l * m * t <= 0 && s[mid] <= t) {
                        ans = mid;
                        low = mid + 1;
                    }
                    else
                        hi = mid - 1;
                }
                out.println(ans < 0 ? ans : ans + 1);
            }
        }

        class ShortScanner {
            Scanner in;

            ShortScanner(Scanner in) {
                this.in = in;
            }

            int i() {
                return in.nextInt();
            }

        }

    }
}
