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.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class Main {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    static PrintWriter writer;

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

    static long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    static boolean eof = false;

    static String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    public static void main(String[] args) throws IOException {
        tokenizer = null;
        // reader = new BufferedReader(new FileReader("grave.in"));
        // writer = new PrintWriter(new FileWriter("grave.out"));
        reader = new BufferedReader(new InputStreamReader(System.in, "ISO-8859-1"));
        writer = new PrintWriter(System.out);
        banana();
        reader.close();
        writer.close();
    }

    static boolean test(long l, long r, long t, long m, long a, long b) {
        if ((a + (r - 1) * b) > t)
            return false;
        
        long sum = (r - l + 1) * (2 * a + (l + r-2) * b) / 2;
        
        if (sum > t * m)
            return false;
        
        return true;
    }

    static void banana() throws IOException {
        long a = nextLong();
        long b = nextLong();
        long n = nextLong();

        for (int i = 0; i < n; ++i) {
            long l = nextInt();
            long ll = l;
            long t = nextInt();
            long m = nextInt();

            if (a + (l - 1) * b > t) {
                writer.println(-1);
                continue;
            }

            long rr = 1000000000;

            while (rr - ll > 1) {
                long mid = (rr + ll) / 2;

                if (test(l, mid, t, m, a, b))
                    ll = mid;
                else
                    rr = mid;
            }
            if (test(l, rr, t, m, a, b))
                writer.println(rr);
            else
                writer.println(ll);

        }
    }
}