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.*;
import java.io.*;
public class A
{
	public static void main(String[] args) throws Exception
	{
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		long a = in.nextInt();
		long b = in.nextInt();
		int n = in.nextInt();
		
		for(int x = 0; x < n; x++)
		{
			long l = in.nextInt() - 1;
			long t = in.nextInt();
			long m = in.nextInt();
			
			long low = l;
			long high = t + 2;
			while(low < high)
			{
				long mid = (low + high + 1) / 2;
				
				if(check(a, b, l, mid, t, m))
				{
					low = mid;
				}
				else
				{
					high = mid - 1;
				}
			}
			
			if(!check(a, b, l, low, t, m))
			{
				System.out.println(-1);
			}
			else
			{
				System.out.println(low + 1);
			}
		}
	}
	
	public static boolean check(long a, long b, long l, long r, long t, long m)
	{
		if(a + b * r > t)
		{
			return false;
		}
		
		long sum = a * (r - l + 1) + ((b * (r - l + 1) * (r + l)) / 2);
		
		return sum <= t * m;
	}
	
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;
		
		public FastScanner(InputStream input)
		{
			br = new BufferedReader(new InputStreamReader(input));
			st = new StringTokenizer("");
		}
		
		public String next() throws IOException
		{
			if(st.hasMoreTokens())
			{
				return st.nextToken();
			}
			else
			{
				st = new StringTokenizer(br.readLine());
				return next();
			}
		}
		
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
		}
	}
}
