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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Tavas {

	static double A, B, N;
	
	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		String[] inf = br.readLine().split(" ");
		A = Double.parseDouble(inf[0]);
		B = Double.parseDouble(inf[1]);
		N = Double.parseDouble(inf[2]);
		
		int[] respostas = new int [(int)N];
		
		for (int i = 0; i < N ; i++){
			String[] dados = br.readLine().split(" ");
			double L = Double.parseDouble(dados[0]);
			double T = Double.parseDouble(dados[1]);
			double M = Double.parseDouble(dados[2]);
			
			int R = findR(L , T, M);
			
			respostas[i] = R;
			
		}
		
		for (int i = 0; i < N ; i++){
			System.out.println(respostas[i]);
		}
	}

	
	
	
	private static int findR(double l, double t, double m) {
		int hi = (int) (((double)(t-A)/(double)B) + 1.5);
		int lo = (int) l;
		if (!isEatable(l, t, m , l) || hi < lo){
			return -1;
		}
		while (lo +1 < hi){
			int mid = (int) (((double)(hi)+ (double)(lo))/2d);
			if(isEatable(l, t, m , mid)){
				lo = mid ;				
			} else {
				hi = mid ;
			}
		}
		if (!isEatable(l, t, m, (hi+lo)/2 + 1)){
			hi = lo;
		}
		return hi;
	}

	private static boolean isEatable(double l , double t, double m, double r){
		double number = ((A+(B*(l-1d))+(A+(B*(r-1d))))/2d) * (r-l+1d);
		if ((number <= (m *t)) && (A+B*(r-1)) <= t ){
			return true;
		} else {
			return false;
		}
	}
}
