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.BufferedReader;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class Main {
	public static int A,B,n;
	public static long psum(long start, long end){
		return (long) (end - start + 1) * ((long)A + (start - 1) * (long)B + (long)A + (end - 1) * (long)B) / 2;
	}
	
	public static void main(String[] argv) {
		FastScanner scan = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		A = scan.nextInt();
		B = scan.nextInt();
		n = scan.nextInt();
		
		for(int i = 0; i < n; ++i){
			int l = scan.nextInt();
			int t = scan.nextInt();
			int m = scan.nextInt();
			
			long left = l;
			long right = 1000000000000L;
			//System.out.println(right);
			long ret = l;
			while(left <= right){
				
				long mid = (left + right) / 2;
				//System.out.println(left + " / " + right + " / " + mid);
				long p = psum(l, mid);
				long rightval = (long)A + (mid - 1) * (long)B;
				long cnt = p / m;
				if(cnt * m < p) cnt++;
				
				if(cnt < rightval){
					cnt = rightval;
				}
				
				if(cnt <= (long) t){
					left = mid + 1;
					ret = mid;
				} else {
					right = mid - 1;
				}
			}
			if(right == l - 1) System.out.println(-1);
			else System.out.println(ret);
		}
		
		out.close();
	}

	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		FastScanner(InputStream is) {
			try {
				br = new BufferedReader(new InputStreamReader(is));
			} catch (Exception e) {
				e.printStackTrace();
			}
		}

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

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.valueOf(next());
		}
	}
}