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.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.PrintStream;
import java.util.Scanner;

public class CF3 {
public static void main(String args[]) throws FileNotFoundException{
	Scanner sc=new Scanner(System.in);
//	PrintStream out = new PrintStream(new FileOutputStream("C:/Users/z00191f/Downloads/output.txt"));
//	System.setOut(out);
	long A=sc.nextLong();
	long B=sc.nextLong();
	int n=sc.nextInt();
	for(int i=0;i<n;i++){
		long l=sc.nextLong();
		long t=sc.nextLong();
		long m=sc.nextLong();
		if(A+(l-1)*B>t){
			System.out.println(-1);
			continue;
		}else if(A+(l+m-2)*B>=t){
			long lo=l;
			long hi=l+m-1;
			long mid=hi;
			while(lo!=mid){
				if(A+B*(mid-1)<=t){
					lo=mid;
				}else{
					hi=mid;
				}
				mid=(lo+hi)/2;
				//System.out.println(lo+" "+hi+" "+mid+" "+(A+B*(mid-1)));
			}
			System.out.println(mid);
		}else{
			long lo=l+m-1;
			long hi=(long) (1e6+5);
			long mid=hi;
			while(lo!=mid){
				if(A+(mid-1)*B>t){
					hi=mid;
				}else if(sum(A+(l-1)*B,B,mid-l+1)<=m*t){
					lo=mid;
				}else{
					hi=mid;
				}
				mid=(lo+hi)/2;
				//System.out.println(lo+" "+hi);
			}
			System.out.println(mid);
		}
	}
}
public static long sum(long A,long B,long m){
	return (2*A+(m-1)*B)*m/2;
}
}
