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.*;

public class C {
    public static void main(String args[]) throws FileNotFoundException {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        new Solver().solve(in, out);
        out.close();
    }
}

class Solver{
	int A, B;
	public void solve(InputReader in, PrintWriter out){
    	A = in.nextInt(); B = in.nextInt();
    	int N = in.nextInt();
    	for(int i=0; i<N; i++){
    		long l = in.nextInt(), t = in.nextInt(), m = in.nextInt();

    		int res = upperBound(l, t, t*m);
    		out.println(res >= l ? res : -1);
    	}
	}

	long getSum(long endIndex){
		return endIndex*A+(endIndex-1)*endIndex/2*B;
	}

	public int upperBound(long left, long maxHeight, long maxRemoveAble){
        long mid, start = 0, end = 1000000;
        while(start != end){
            mid = (start+end+1)/2;
            if(A+(mid-1)*B > maxHeight || getSum(mid)-getSum(left)+(A+(left-1)*B) > maxRemoveAble)  end = mid-1;
            else start = mid;
        }
        return (int)start;
    }
}


class InputReader {
    public BufferedReader reader;
    String currentLine[];
    int token;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        currentLine = null;
        token = 0;
    }

    public String next(){
        while (currentLine == null || token >= currentLine.length) {
            try {
                currentLine = reader.readLine().split("\\s+");
                token = 0;
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return currentLine[token++];
    }

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

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