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.

<image>

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 A {
    FastScanner in;
    PrintWriter out;

    long a;
    long b;

    long get(long i) {
        return a + b * (i - 1);
    }

    long getSum(long l, long r) {
        long k = (r - l + 1);
        return get(l) * k + b * (k - 1) * k / 2;
    }

    public void solve() throws IOException {
        a = in.nextInt();
        b = in.nextInt();
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            int l = in.nextInt();
            long t = in.nextInt();
            long m = in.nextInt();
            if (get(l) > t) {
                out.println(-1);
                continue;
            }
            long left = l;
            long right = left + (t - a) / b + 20;
            while (left < right - 1) {
                long med = (left + right) / 2;
                //System.err.println(left + " " + right + " " + getSum(l, med) + " " + (t * m));
                if (get(med) > t || getSum(l, med) > t * m) {
                    right = med;
                } else {
                    left = med;
                }
            }
            out.println(left);
        }

    }

    public void run() {
        try {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
            Locale.setDefault(Locale.US);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner(InputStream f) {
            br = new BufferedReader(new InputStreamReader(f));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    public static void main(String[] arg) {
        new A().run();
    }
}