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.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

import static java.lang.Math.*;

public class solver implements Runnable {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    public static void main(String[] args) {
        new Thread(null, new solver(), "", 256 * (1L << 20)).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            init();
            solve();
            out.close();
            time();
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }
    
    int a;
    int b;
    
    long getValue(int x) {
        return a + (long)(x - 1) * b;
    }
    
    long calcArythm(long from, long to, int cnt) {
        return (from + to) * cnt / 2;       
    }
    
    boolean check(int l, int r, int t, int m) {
       long x = getValue(l);
       long y = getValue(r);
       return y <= t && calcArythm(x, y, r-l+1) <= (long)m * t;
    }

    void solve() throws IOException {
        a = readInt();
        b = readInt();
        int n = readInt();
        
        for (int i=0;i<n;i++) {
            int l = readInt();
            int t = readInt();
            int m = readInt();
            
            int left = 0;
            int right = (int)1e6;
            right *= 4;
            int answer = -1;
            while (left <= right) {
                int mid = (left + right) / 2;
                if (check(l, l + mid, t, m)) {
                    answer = l + mid;
                    left = mid + 1;
                } else {
                    right = mid - 1;
                }
            }
            
            out.println(answer);
        }       
    }
}