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.*;
import java.util.*;

public class c1 {
	public static void main(String[] args) throws FileNotFoundException {
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		long a = in.nextInt();
		long b = in.nextInt();
		int n = in.nextInt();
		for (int i = 0; i < n; i++) {
			long l = in.nextInt();
			long t = in.nextInt();
			long m = in.nextInt();
			long r = t + 1 + l + m + t + m;
			long startl = l;
			if ((long)(a + 1l * b * (l - 1)) >= t + 1){
				out.println(-1);
			}
			else{
				while (l + 1 != r){
					long mid = (l + r) / 2;
					long last = 1l * (mid - 1) * b + a;
					long first = 1l * (startl - 1) * b + a;
					long sum = (1l * (last + first) * (mid - startl + 1)) / 2;
					if (last <= t && sum <= 1l * t * m){
						l = mid;
					}
					else{
						r = mid;
					}
				}
				out.println(l);
			}
		}
		out.close();
	}
}