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.util.*;

public class cf_03 {

    public static void main(String[] args) {
        // TODO Auto-generated method stub
        Scanner sc=new Scanner(System.in);
        long A=sc.nextInt();
        long B=sc.nextInt();
        long n=sc.nextInt();
        while(n>0){
            n--;
            long l=sc.nextInt();
            long t=sc.nextInt();
            long m=sc.nextInt();
            if(A+(l-1)*B>t){
                System.out.println("-1");
                continue;
            }
            long a=B;
            long b=2*A-B;
            long c=2*A-B*(long)Math.pow(l, 2)+3*B*l-2*B-2*m*t-2*A*l;
            long temp=(long)Math.sqrt((long)Math.pow(b, 2)-4*a*c);
            long result=(-b+temp)/(2*a);
            if((A+(result-1)*B)>t)
                System.out.println((t-A)/B+1);
            else
                System.out.println(result);
        }
        return;
    }

}
