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.

<image>

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 TavasAndKarafs {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(in.readLine());
		long A = Long.parseLong(st.nextToken());
		long B = Long.parseLong(st.nextToken());
		long n = Long.parseLong(st.nextToken());
		for (int i = 0; i < n; i++) {
			st = new StringTokenizer(in.readLine());
			long l = Long.parseLong(st.nextToken());
			long t = Long.parseLong(st.nextToken());
			long m = Long.parseLong(st.nextToken());
			long lo = l, hi = 1;
			while (possible(A, B, l, hi, t, m)) hi *= 2;
			while (lo < hi) {
				long mid = lo + (hi - lo + 1)/2;
				if (possible(A, B, l, mid, t, m)) {
					lo = mid;
				} else {
					hi = mid - 1;
				}
			}
			if (!possible(A, B, l, l, t, m)) {
				out.println(-1);
			} else {
				out.println(lo);
			}
		}
		
		in.close();
		out.close();
	}
	
	public static boolean possible(long A, long B, long l, long r, long t, long m) {
		return calc(A, B, r) <= t && sum(A, B, l, r) <= t*m;
	}
	
	public static long calc(long A, long B, long i) {
		return A + B*(i-1);
	}
	
	public static long sum(long A, long B, long l, long r) {
		return (r-l+1)*A + B*((r-l+1)*(l-1+r-1)/2);
	}
}
