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 C {
	
	public static void main(String[] args) throws Exception {
		int dex = 0;
		FastScanner qwe = new FastScanner(System.in);
		long A = qwe.nextLong();
		long B = qwe.nextLong();
		
		int n = qwe.nextInt();
		
		PrintWriter out = new PrintWriter(System.out);
		
		while(n-->0){
			
			long l = qwe.nextInt();
			long t = qwe.nextInt();
			long m = qwe.nextInt();
			
			long start =A + B*(l-1);
						
			if(start > t){
				out.println(-1);
			}
//			else if(A+B*(l-1+m-1) > t){
//				
//				long delta = t - start;
//				out.println(l+delta/B);
//				
//			}
			else{
				long bites = t*m;
				long min = 0;
				long max = 10_000_000l;
				
				while(min+1 < max){
					long med = (min + max)/2;
					boolean good = true;
					
					if(start+B*med > t) good = false;
					
					else if ((med+1)*(2*start+med*B)/2 > bites) good=  false;
					if(good){
						//can do it
						min = med;
					}
					else{
						max = med;
					}
				}
				
				out.println(l+min);
				
			}
			
		}
				
		out.close();				
	}
	
	
	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		
		public FastScanner(InputStream in) throws Exception{
			br = new BufferedReader(new InputStreamReader(in));
			st = new StringTokenizer(br.readLine().trim());
		}
		public int numTokens() throws Exception {
			if(!st.hasMoreTokens()){
				st = new StringTokenizer(br.readLine().trim());
				return numTokens();
			}
			return st.countTokens();
		}
		public String next() throws Exception {
			if(!st.hasMoreTokens()){
				st = new StringTokenizer(br.readLine().trim());
				return next();
			}
			return st.nextToken();
		}
		public double nextDouble() throws Exception{
			return Double.parseDouble(next());
		}
		public float nextFloat() throws Exception{
			return Float.parseFloat(next());
		}
		public long nextLong() throws Exception{
			return Long.parseLong(next());
		}
		public int nextInt() throws Exception{
			return Integer.parseInt(next());
		}
		public String nextLine() throws Exception{
			return br.readLine().trim();
		}
	}

}
