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.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Random;
import java.util.StringTokenizer;

public class TavasandKarafs {

  static BufferedReader in;
  static PrintWriter out;
  static StringTokenizer tok;

  static void solve() throws Exception {
    long A = nextLong();
    long B = nextLong();
    long n = nextLong();
    while (n-- > 0) {
      long l = nextLong();
      long t = nextLong();
      long m = nextLong();
      long r = (t - A) / B + 2;
      long copyL = l;
      long valueL = A + (l - 1) * B;
      if (valueL > t) {
        out.println(-1);
        continue;
      }
      while (r - l > 1) {
        long mid = (l + r) >>> 1;
        long valueMid = A + (mid - 1) * B;
        long sum = (valueL + valueMid) * (mid - copyL + 1) / 2;
        if (sum <= t * m)
          l = mid;
        else
          r = mid;
      }
      out.println(l);
    }
  }

  public static void main(String args[]) {
    try {
      in = new BufferedReader(new InputStreamReader(System.in));
      out = new PrintWriter(new OutputStreamWriter(System.out));
      solve();
      in.close();
      out.close();
    } catch (Throwable e) {
      e.printStackTrace();
      System.exit(1);
    }
  }

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

  static int[] nextIntArray(int len, int start) throws IOException {
    int[] a = new int[len];
    for (int i = start; i < len; i++)
      a[i] = nextInt();
    return a;
  }

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

  static long[] nextLongArray(int len, int start) throws IOException {
    long[] a = new long[len];
    for (int i = start; i < len; i++)
      a[i] = nextLong();
    return a;
  }

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

  static double[] nextDoubleArray(int len, int start) throws IOException {
    double[] a = new double[len];
    for (int i = start; i < len; i++)
      a[i] = nextDouble();
    return a;
  }

  static BigInteger nextBigInteger() throws IOException {
    return new BigInteger(next());
  }

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

  static String nextLine() throws IOException {
    tok = new StringTokenizer("");
    return in.readLine();
  }

  static void shuffleArray(long[] array) {
    Random random = new Random();
    for (int i = array.length - 1; i > 0; i--) {
      int index = random.nextInt(i + 1);
      long temp = array[index];
      array[index] = array[i];
      array[i] = temp;
    }
  }

  static boolean hasNext() throws IOException {
    while (tok == null || !tok.hasMoreTokens()) {
      String s = in.readLine();
      if (s == null) {
        return false;
      }
      tok = new StringTokenizer(s);
    }
    return true;
  }

}
