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

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskA {
    /*RE*/
    long sum(long L, long R, long A, Long B) {
        return (R - L + 1) * (A + (L - 1) * B + A + (R - 1) * B) / 2;
    }
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        long A = in.nextLong();
        long B = in.nextLong();
        int n = in.nextInt();
        while ((n--) != 0) {
            long L = in.nextLong(); 
            long t = in.nextLong(); 
            long m = in.nextLong();
            if (A + (L - 1) * B > t) {
                out.println(-1);
                continue;
            }
            /*
            Long tl = L, tr = (t - A) / B + 1;
            while (tl <= tr) {
                Long mid = (tl + tr) / 2; 
                if (sum(L, mid, A, B) < t * m) tl = mid + 1;
                else if (sum(L, mid, A, B) > t * m) tr = mid - 1;
            }
            out.println(tr);
            */
            long tl = L, tr = (t - A) / B + 2;
            while (tr - tl > 1) {
                long mid = (tl + tr) / 2;
                if (sum(L, mid, A, B) <= t * m) tl = mid;
                else tr = mid;
            }
            out.println(tl);
        }
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

    public long nextLong() {
        return Long.parseLong(next());
    }

}