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.io.*;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.*;

public class SolveContest {
    private BufferedReader in;
    private PrintWriter out;

    public SolveContest() {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter(new FileWriter("output.txt"),true);
            solve();
        } catch (Exception e) {
            e.printStackTrace();
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
            solve();
        } finally {
            try {
                in.close();
            } catch (IOException e) {

            }
            out.close();
        }
    }
    StringTokenizer st;
    String nextToken()
    {
        while (st == null || !st.hasMoreTokens())
            try {
                st = new StringTokenizer(in.readLine());
            } catch (IOException e) {

            }
        return st.nextToken();
    }
    int nextInt() {
        return Integer.valueOf(nextToken());
    }
    long nextLong() {
        return Long.valueOf(nextToken());
    }


    public void solve() {
        long a = nextInt();
        long b = nextInt();
        int n = nextInt();
        int size = 2000000;
        for (int i = 0; i < n; i++) {
            int llf = nextInt();
            int lf = 0;
            int tt = nextInt();
            long m = nextInt();
            int r = size;
            while (r - lf > 1) {
                int x = (r + lf) / 2;
                if (((a + (llf-1)*b)+(a+(x-1)*b))*(x-llf+1)/2 <= m * tt && (a+(x-1)*b <= tt)) {
                    lf = x;
                } else {
                    r = x;
                }
            }
            if (lf < llf) {
                out.println(-1);
            } else {
                out.println(lf);
            }
        }
    }

    public static void main(String[] args) {
        new SolveContest();
    }
}