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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        QuickScanner in = new QuickScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskA {
    long A,B;
    public long getI(long i)
    {
        return A+(i-1)*B;
    }
    public long sum(long n)
    {
        return n*A+(n-1)*n/2*B;
    }
    public void solve(int testNumber, QuickScanner in, PrintWriter out) {
        A=in.nextInt();
        B=in.nextInt();
        int n=in.nextInt();
        while(n-->0)
        {
            long l, t, m;
            l=in.nextInt();
            t=in.nextInt();
            m=in.nextInt();
            if(getI(l)>t)
            {
                out.println(-1);
                continue;
            }
            long lb=l;
            long rb=1000000;
            while(lb<rb)
            {
                long c=(lb+rb+1)/2;
                if(getI(c)<=t && sum(c)-sum(l-1)<=m*t)
                    lb=c;
                else
                    rb=c-1;
            }
            out.println(rb);
        }
    }
}

class QuickScanner {
    BufferedReader in;
    StringTokenizer token;
    String delim;
    public QuickScanner(InputStream inputStream)
    {
        this.in=new BufferedReader(new InputStreamReader(inputStream));
        this.delim=" \n\t";
        this.token=new StringTokenizer("",delim);
    }

    public boolean hasNext()
    {
        while(!token.hasMoreTokens())
        {
            try {
                String s=in.readLine();
                if(s==null) return false;
                token=new StringTokenizer(s,delim);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        return true;
    }

    public String next()
    {
        hasNext();
        return token.nextToken();
    }

    public int nextInt()
    {
        return Integer.parseInt(next());
    }

}
