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
/**
 * Created by Martin on 11/16/2016.
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.PrintWriter;

public class Main {

    public static void main(String[]args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());
        int A = Integer.parseInt(st.nextToken());
        long B = Integer.parseInt(st.nextToken());
        int N = Integer.parseInt(st.nextToken());

        while (N-- > 0) {
            st = new StringTokenizer(br.readLine());
            int l = Integer.parseInt(st.nextToken());
            int t = Integer.parseInt(st.nextToken());
            int m = Integer.parseInt(st.nextToken());

            long tof = t * ((long) m);
            long aL = A + (l - 1) * B;
            if (aL > t) {
                pw.println(-1);
            }
            else {
                int high = (int) (((t - A) / B + 1) + 1);
                int low = l;
                while (low < high) {

                    int mid = (low + high) / 2;
                    long aM = A + (mid - 1) * B;
                    long sumat = ((mid - l + 1) * (aL + aM)) / 2;
                    //debug(low, high, sumat, tof);
                    if (sumat < tof) {
                        low = mid + 1;
                    }
                    else {
                        high = mid;
                    }
                }
                long aM = A + (low - 1) * B;
                long sumat = ((low - l + 1) * (aL + aM)) / 2;
                if (sumat != tof) low--;
                pw.println(low);
            }
        }
        pw.flush();

    }

    public static void debug(Object...args) {
        System.out.println(Arrays.deepToString(args));
    }
}

