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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

/**
 * Created by mostafa on 9/27/17.
 */
public class TavasKarafs {

    static int A, B;
    static long[] acc;
    static boolean can(int l, int r, int m, int t) {
        long needed = acc[r] - acc[l - 1];
        long cur = A + 1l * (r - 1) * B;

        return needed <= 1l * m * t && t >= cur;
    }

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner();
        A = sc.nextInt(); B = sc.nextInt();
        int n = sc.nextInt();
        acc = new long[(int) 1e7];
        for(int i = 1; i < acc.length; i++) {
            acc[i] = acc[i - 1] + A + (i - 1) * B;
        }

        PrintWriter out = new PrintWriter(System.out);
        while(n-->0) {
            int l = sc.nextInt(), t = sc.nextInt(), m = sc.nextInt();

            int low = l, high = acc.length;
            int ans = -1;
            while(low <= high) {
                int mid = (low + high) / 2;
                if(can(l, mid, m, t)) {
                    ans = mid;
                    low = mid + 1;
                }
                else
                    high = mid - 1;
            }

            out.println(ans);
        }

        out.flush();
        out.close();
    }

    static class Scanner {
        BufferedReader br;
        StringTokenizer st;
        Scanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() throws IOException {
            while(st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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