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 A {

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;
	boolean eof;

	int f(int A, int B, int low, int cnt, int size) {
		int just = Math.floorDiv(cnt - A, B) + 1;
		if (just < low) {
			return -1;
		}
		int initLow = low;
		int high = just + 1;
		while (high - low > 1) {
			int mid = (low + high) / 2;
			long total = ((2 * A + (long) B * (initLow - 1 + mid - 1)))
					* (mid - initLow + 1) / 2;
//			System.err.println(mid + " " + total);
			if (total <= (long) cnt * size) {
				low = mid;
			} else {
				high = mid;
			}
//			System.err.println(low + " " + high);
		}
		return low;
	}

	void solve() throws IOException {
		int A = nextInt();
		int B = nextInt();
		int q = nextInt();
		for (int i = 0; i < q; i++) {
			int low = nextInt();
			int cnt = nextInt();
			int size = nextInt();
			out.println(f(A, B, low, cnt, size));
		}
	}

	A() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new A();
	}

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return null;
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			eof = true;
			return null;
		}
	}

	int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}