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
//535C

import java.util.Scanner;

public class TavasAndKarafs {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		int n = sc.nextInt();
		
		for (int _ = 0; _ < n; _++) {
			int l = sc.nextInt();
			int t = sc.nextInt();
			int m = sc.nextInt();
			
			int i = l-1;
			int j = (t-a)/b+2;
			
			for (int k = (i+j+1)/2; i < j-1; k = (i+j+1)/2) {
				if (edible(a,b,l,k,t,m)) {
					i = k;
				}
				else {
					j = k;
				}
			}
			if (i == l-1)
				System.out.println(-1);
			else
				System.out.println(i);
		}
	}

	private static boolean edible(int a, int b, long l, long r, int t, int m) {
		if (m >= r - l + 1) {
			return t >= a + b * (r - 1);
		}
		long total = a * (r - l + 1) + b * (r * (r - 1) - (l - 1) * (l - 2)) / 2L;
		total = (total + m - 1) / m;
		if (total <= a + b * (r - 1)) {
			total = a + b * (r - 1);
		}
		return t >= total;
	}
}
