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.*;
import java.util.*;

public class Main {

    private static PrintWriter out;
    private static FastReader in;

    private static int[][] boxes;

    private static int[] order;
    private static int position;
    private static boolean[] used;

    private static class FastReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public FastReader(InputStream inputStream) {
            reader = new BufferedReader(
                    new InputStreamReader(inputStream), 1 << 16);
            tokenizer = null;
        }

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

        public String nextLine() {
            try {
                return reader.readLine();
            }
            catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        }

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

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

        public double nextDouble() {
            return Double.parseDouble(in.next());
        }
    }

    public static void main(String[] args) throws FileNotFoundException {
        //in = new FastReader(new FileInputStream("input.txt"));
        //out = new PrintWriter(new FileOutputStream("output.txt"));
        in = new FastReader(System.in);
        out = new PrintWriter(System.out);

        int a = in.nextInt(), B = in.nextInt();
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            int l = in.nextInt();
            int t = in.nextInt(), m = in.nextInt();
            long A = a; A += (long)(l - 1) * B;
            long left = 0, right = ((long)t - A) / B;
            while (left <= right) {
                long mid = (left + right + 1) / 2;
                if ((mid + 1) * A + mid * (mid + 1) / 2 * B <= (long)m * t) {
                    left = mid;
                    if (left == right) break;
                }
                else {
                    right = mid - 1;
                }
            }
            out.println((left == right) ? left + l : -1);
        }

        out.flush();
    }

}