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.*;
import java.util.*;
public final class xor_equation
{
    static FastScanner sc=new FastScanner(new BufferedReader(new InputStreamReader(System.in)));
    static PrintWriter out=new PrintWriter(System.out);
	
	public static void main(String args[]) throws Exception
	{
		long a=sc.nextLong(),b=sc.nextLong(),n=sc.nextLong();
		for(int i=1;i<=n;i++)
		{
			long l=sc.nextLong(),t=sc.nextLong(),m=sc.nextLong(),first=a+((l-1)*b);
			if(t<first)
			{
				out.println(-1);
			}
			else
			{
				long low=l,high=(long)Math.pow(10,6);
				while(low<high)
				{
					long mid=(low+high+1)>>1,curr_val=a+((mid-1)*b);
					if(curr_val<=t)
					{
						long sum=((mid-l+1)*(first+curr_val))/2;
						long now=Math.max(curr_val,sum/m+((sum%m==0)?0:1));
						if(now<=t)
						{
							low=mid;
						}
						else
						{
							high=mid-1;
						}
					}
					else
					{
						high=mid-1;
					}
				}
				out.println(low);
			}
		}
		out.close();
	}
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}