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.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class R299C {
	public static void main(String[] args) {
		FastScanner in=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		long a=in.nextLong();
		long b=in.nextLong();
		long n=in.nextLong();
		while(n-->0){
			long l=in.nextLong();
			long t=in.nextLong();
			long m=in.nextLong();
			long lo=0;
			long hi=1000005;
			while(lo<hi){
				long mid=lo+((hi-lo)>>1);
				if(a+b*(mid-1)>t||a*(mid-l+1)+b*(mid*(mid-1)-(l-1)*(l-2))/2>t*m)
					hi=mid;
				else
					lo=mid+1;
			}
			if(hi-1<l)
				out.println(-1);
			else
				out.println(hi-1);
		}
		out.flush();
		
	}
	static class FastScanner{
		BufferedReader br;
		StringTokenizer st;
		public FastScanner(){br=new BufferedReader(new InputStreamReader(System.in));}
		String nextToken(){
			while(st==null||!st.hasMoreElements())
				try{st=new StringTokenizer(br.readLine());}catch(Exception e){}
			return st.nextToken();
		}
		int nextInt(){return Integer.parseInt(nextToken());}
		long nextLong(){return Long.parseLong(nextToken());}
		double nextDouble(){return Double.parseDouble(nextToken());}
	}
}
