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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.TreeSet;


public class D {
	static IR in = new IR(System.in);
	static long A,B;
	static int q;
	static long l,t,m;
	static long oo = 31221331823L;
	static PrintWriter out = new PrintWriter(System.out);

	static long sum(long r)
	{
		
		return r*(r-1)/2;
	}
	static boolean can(long r)
	{

		long curr = A+(r-1)*B;
		long sum = B*(sum(r)-sum(l-1));
		sum += A*(r-l+1);
		
		
		return (t>=curr)&&m*t>=sum;

	}
	public static void main(String[]args)throws Throwable
	{
		A = in.ll(); B = in.ll(); q = in.j();
		long lo = 0;
		long hi = oo;
		long ans = 0;
		while(q-->0)
		{
			l = in.ll(); t = in.ll(); m= in.ll();
			lo = l;
			hi = oo;
			
			ans = -1;
			while(lo<=hi)
			{
				
				long mid = lo+(hi-lo)/2;
				if(can(mid))
				{
					lo = mid+1;
					ans = mid;
				}
				else{
					hi = mid-1;
				}


			}
			out.printf("%d\n",ans);

		}

out.flush();
out.close();
	}







	static	class IR {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public IR(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int j() {
			return Integer.parseInt(next());
		}
		public long ll(){
			return Long.parseLong(next());
		}


	}
}

