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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.StringTokenizer;

// Codeforces Round #299 (Div. 2)
// Tavas and Karafs
public class Problem_535_C {
    

    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Problem_535_C solver = new Problem_535_C();
        solver.solve(1, new InputStreamReader(inputStream), out);
        out.close();
    }

    public void solve(int test, Reader input, PrintWriter out)
    {
        MyScanner in = new MyScanner(input);
        
        int A = in.nextInt();
        int B = in.nextInt();
        int n = in.nextInt();

        for(int i = 0; i < n; i++) {
          int l = in.nextInt();
          int t = in.nextInt();
          int m = in.nextInt();
          
          long a = 0, b = 2 * Math.max(t, m) + 1;
          while (b - a > 1) {
              long q = (a + b) / 2;
              if (A + (l + q - 2) * 1l * B <= t && (A + (l - 1) * 1l * B) * 1l * q + B * 1l * q * (q - 1) / 2 <= m * 1l * t)
                  a = q;
              else
                  b = q;
          }
          out.printf("%d\n", (a == 0) ? -1 : l + a - 1);
        }
    }

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(Reader reader) {
            br = new BufferedReader(reader);
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    //--------------------------------------------------------

}
