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.util.*;
import java.io.*;
 
public class a {
  public static void main(String[] args) {
    InputReader in = new InputReader();
    in.init(System.in);

    Solver soal = new Solver();
    soal.solve(in);
  }
}

class Solver {
  private int a, b, n, l, t, m, r;
  
  public void solve(InputReader in) {
    a = in.nextInt();
    b = in.nextInt();
    n = in.nextInt();

    while (n-- > 0) {
      l = in.nextInt(); 
      t = in.nextInt(); 
      m = in.nextInt();

      r = (t - a) / b + 1;  // U(r) <= t      
      int ans = binser(l, r, m, t);
      System.out.println(ans < l ? -1 : ans);
    }
  }

  private int binser(int l, int r, int m, int t) {
    int mid;
    long lim = (long) m * t;
    while (l < r) {
      mid = (l + r + 1) / 2;
      if (S(mid) - S(this.l - 1) > lim) {
        r = mid - 1;
      } else {
        l = mid;
      }
    }
    return S(r) - S(this.l - 1) > lim ? -1 : r;
  }

  private long S(int n) {
    return (long) n * (n - 1) / 2 * b + a * n;
  }
}

class InputReader {
  private BufferedReader reader;
  private StringTokenizer tokenizer;

  public void init(InputStream input) {
    reader = new BufferedReader(
            new InputStreamReader(input), 
            32768);
    tokenizer = null;
  }

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

  public int nextInt() {
    return Integer.parseInt(next());
  }
  
  public long nextLong() {
    return Long.parseLong(next());
  }
}



