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 TaskC{
    private static boolean canEat(long fst, long b, long i, long m, long t){
        m = Math.min(m, i);
        return (m * t >= fst * i + (i * (i - 1)) / 2 * b) && (t >= fst + (i - 1) * b);
    }
    public static void main(String args[]) throws IOException{
        Reader reader = new BufferedReader(new InputStreamReader(System.in));
        StreamTokenizer in = new StreamTokenizer(reader);

        in.nextToken();
        long a = (long)in.nval;
        in.nextToken();
        long b =(long)in.nval;

        in.nextToken();
        int  n = (int)in.nval;

        for (int q = 0; q < n; q++){
            in.nextToken();
            long left = (long)in.nval;
            in.nextToken();
            long t = (long)in.nval;
            in.nextToken();
            long m = (long)in.nval;

            long fst = a + b * (left - 1);

            long r = 1;
            while (canEat(fst, b, r, m, t))
                r *= 2;

            long l = 1;


            while (r - l > 1){
                long mid = (l + r) / 2;
                if (canEat(fst, b, mid, m, t))
                    l = mid;
                else
                    r = mid;
            }
            if (fst <= t)
                System.out.println(left + l - 1);
            else
                System.out.println(-1);
        }

        reader.close();
    }
}
