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

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);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}

	static class Task {

		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();

				long lo = l - 1;
				long hi = (long) 10e10;

				while (lo < hi) {
					long r = lo + (hi - lo) / 2;
					boolean canEat = eatable(a, b, m, l, r, t); //can eat within t - m bites
					if (lo == hi - 1)
					{
						if(eatable(a,b,m,l,hi,t))
							lo = hi;
						break;
					}
					if (canEat)
						lo = r;
					else
						hi = r - 1;
				}


				if (lo < l)
					out.println(-1);
				else
					out.println(lo);


			}

		}

	}

	public static boolean eatable(long a, long b, long m, long l, long r, long t) {
		long sum = a * (r - l + 1) + b * ((r * (r - 1)) / 2 - ((l - 1) * (l - 2)) / 2);
		long hn = a + (r - 1) * b;

		return hn <= t && sum <= m * t;
	}


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

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

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

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

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

	}
}