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.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Random;
import java.util.StringTokenizer;

public class Contest {

	static final Random random = new Random();

	static PrintWriter out = new PrintWriter(System.out);

	public static void main(String[] args) throws FileNotFoundException {
		Scanner sc = new Scanner(System.in);

		long A = sc.nextLong(), B = sc.nextLong();
		int n = sc.nextInt();

		long[] s = new long[(int) 1e6 + 1];

		for (int i = 1; i <= (1e6); i++) {
			s[i] = B * (i - 1) + A;
			s[i] += s[i - 1];
		}

		while (n-- > 0) {
			int L = sc.nextInt();
			long t = sc.nextLong(), m = sc.nextLong();
//			long tot = t * m;

			int l = L, r = (int) 1e6, ans = -1;

			while (l <= r) {
				int mid = l + (r - l) / 2;
//				System.out.println(sum(L, mid, s) + " " +  (long)Math.min((mid-L+1),m)*t);
				if (sum(L, mid, s) <= (long) Math.min((mid - L + 1), m) * t && (s[mid] - s[mid - 1]) <= t) {
					ans = mid;
					l = mid + 1;
				} else {
					r = mid - 1;
				}
			}
			out.println(ans);
		}

		out.flush();
	}

	static long sum(int l, int r, long[] s) {
		return s[r] - s[l - 1];
	}

	static void Arrayssort(int[] a) {
		int n = a.length;// shuffle, then sort
		for (int i = 0; i < n; i++) {
			int oi = random.nextInt(n);
			int temp = a[oi];
			a[oi] = a[i];
			a[i] = temp;
		}
		java.util.Arrays.sort(a);
	}

	private static class Scanner {
		public BufferedReader reader;
		public StringTokenizer st;

		public Scanner(InputStream file) throws FileNotFoundException {
			reader = new BufferedReader(new InputStreamReader(file));
			st = null;
		}

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

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

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

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

		public String nextLine() throws IOException {
			return reader.readLine();
		}
	}

}