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.Scanner;

public class TavasAndKarafs 
{
	static long a, b;
	static boolean debug = false;
	
	static long omnom(long l, long t, long m)
	{
		long base = a + ((l-1)*b); //height of leftmost veg.
		if(t < base)
		{
			return -1;
		}
		
		long abmax = t * m;
		
		int pos = 500000;
		int min = 1;
		int max = 1000000;
		
		while(min != max)
		{
//			System.out.println("min " + min + " max " + max);
			pos = (max+min)/2;
			if((max+min)%2 == 1 && max == min+1)pos++;
			long posh = a + ((pos-1)*b);
			if(gettotalcost(l,pos) > abmax || posh > t)
			{ //too big
//				System.out.println("BIG");
				max = pos-1;
			}
			else if(min != max)
			{
				min = pos;
			}
		}
		return min;
	}
	
	static long gettotalcost(long l, long r)
	{
//		System.out.println("l r " + l + " " + r);
		long lheight = a + ((l-1)*b);
//		long rheight = a + ((r-1)*b);
		
		long base = lheight;
		long tot = 0;
		tot += base * (r-l+1);
		
		long hor = r-l;
		tot += ((hor*hor+hor)/2)*b;
		
		return tot;
	}
	
	public static void main(String[] args) 
	{
		Scanner sc = new Scanner(System.in);
		
		a = sc.nextInt();
		b = sc.nextInt();
		
		int n = sc.nextInt();
		
		for(int i = 0; i < n; i++)
		{
			long l = sc.nextInt(); //left
			long t = sc.nextInt(); //bite times
			long m = sc.nextInt(); //bite width
			
			long res = omnom(l,t,m);
			System.out.println(res);
		}

	}

}
