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.

<image>

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 javafx.util.Pair;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        ConsoleIO io = new ConsoleIO();
        new Main(io).solve();
        io.flush();
    }
    ConsoleIO io;
    Main(ConsoleIO io) {
        this.io = io;
    }


    public void solve() {
        int[] ar = io.readIntArray();
        int A = ar[0];
        int B = ar[1];
        int n = ar[2];
        for(int i = 0;i<n;i++){
            ar = io.readIntArray();
            long left = ar[0];
            long t = ar[1];
            long m = ar[2];

            long v = (t-A)/B + 1;

            long suml = A*(left-1)+B*((left-1)*(left-2L)/2);

            long l = 0;
            long r = 2000005;
            while(l<r) {
                long mid = (l + r+1) / 2;
                long z = A * mid + B * (mid * (mid - 1L) / 2) - suml;
                 if (t * m < z) r = mid-1;
                else l = mid;
            }

            long min = Math.min(v,l);

            if(min<left)
                io.writeLine("-1");
            else
                io.writeLine(""+min);
        }
    }

}

class ConsoleIO {
    BufferedReader br;
    PrintWriter out;
    public ConsoleIO(){br = new BufferedReader(new InputStreamReader(System.in));out = new PrintWriter(System.out);}
    public void flush(){
        this.out.close();
    }
    public void writeLine(String s) {
        this.out.println(s);
    }
    public void writeInt(int a) {this.out.print(a);this.out.print(' ');}
    public void writeWord(String s){
        this.out.print(s);
    }
    public String readLine() {try {return br.readLine();}catch (Exception ex){ return "";}}
    public long readLong() {
        return Long.parseLong(this.readLine());
    }
    public int readInt() {
        return Integer.parseInt(this.readLine());
    }
    public int[] readIntArray() {
        String[]n=this.readLine().split(" ");int[]r=new int[n.length];
        for(int i=0;i<n.length;i++)r[i]=Integer.parseInt(n[i]);
        return r;
    }
}

