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.*;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class C{

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            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());
        }

    }

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

    private long binsearch(long sum, long l, long r) {
        if (l > r) return r;
        long mid = (l + r ) /2;
        long block = (el(l) + el(mid)) * (mid - l + 1)/2;
        if ( block - sum <= 0) {
            return binsearch(sum - block, mid + 1, r);
        } else {
            if (l == r)
                return l - 1;
            return binsearch(sum, l, mid);
        }
    }

    private long el(long i) {
        return A + B * (i - 1);
    }
    long A;
    long B;


    public void solve(int testNumber, InputReader in, PrintWriter out) {
        A = in.nextInt();
        B = in.nextInt();
        long n = in.nextInt();

        for (int ci = 0; ci < n; ci++) {
            long l = in.nextInt();
            long t = in.nextInt();
            long m = in.nextInt();
            long r = (t - A) / B + 1;
            long sum = t * m;
            long res = -1;
            //for (long i = l; i <= r && sum > 0 ; i++) {
            //    res = i;
            //    sum -= A + (i - 1) * B;
            //}
            //out.println(sum < 0 ? res - 1 : res);
            if (l > r)
                out.println("-1");
            else
                out.println(binsearch(sum, l, r));
        }





    }

}


