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.io.IOException;

public class Main {
	private static final int MOD = 1000000007;

	public static void main(String[] args) throws Exception {
		long A = nextInt();
		long B = nextInt();
		long Q = nextInt();
		for (int i = 0; i < Q; i++) {
			long l = nextInt();
			long t = nextInt();
			long m = nextInt();

			double a = B;
			double b = 2 * A - B;
			double c = (2 * A + l * B - 2 * B) * (1 - l) - 2 * t * m;
			if (b * b - 4 * a * c < 0) {
				// 虚数解
				System.out.println(-1);
				continue;
			}

			long r = (long) ((-b + Math.sqrt(b * b - 4 * a * c)) / 2 / a);
			long r2 = (t - A) / B + 1;
			r = Math.min(r, r2);
			if (r < l) {
				System.out.println(-1);
				continue;
			}
			System.out.println(r);
		}
	}

	static int nextInt() {
		int c;
		try {
			c = System.in.read();
			while (c != '-' && (c < '0' || c > '9'))
				c = System.in.read();
			if (c == '-')
				return -nextInt();
			int res = 0;
			while (c >= '0' && c <= '9') {
				res = res * 10 + c - '0';
				c = System.in.read();
			}
			return res;
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		return -1;
	}

}