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 C535 {
public static void main(String[] args) throws IOException {
    input.init(System.in);
    PrintWriter out = new PrintWriter(System.out);
    int a = input.nextInt(), b = input.nextInt(), n = input.nextInt();
    int size = 3000001;
    long[] data = new long[size];
    data[0] = a;
    for(int i = 1; i<size; i++) data[i] = b + data[i-1];
    long[] csum = new long[size];
    csum[0] = data[0];
    for(int i= 1; i<size; i++) csum[i] = data[i] + csum[i-1];
    for(int i =0; i<n; i++)
    {
        int l = input.nextInt()-1, t = input.nextInt(), m = input.nextInt();
        int lo = l-1, hi = size;
        while(lo < hi - 1)
        {
            int mid = (lo+hi)/2;
            long sum = csum[mid] - (l == 0 ? 0 : csum[l-1]);
            if(data[mid] <= t && sum <= (long)t*m) lo = mid;
            else hi = mid;
        }
        out.println(lo < l ? -1 : (1+lo));
    }
    out.close();
}

public static class input {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) {
    reader = new BufferedReader(new InputStreamReader(input));
    tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
    while (!tokenizer.hasMoreTokens())
        tokenizer = new StringTokenizer(reader.readLine());
    return tokenizer.nextToken();
    }

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

    static double nextDouble() throws IOException {
    return Double.parseDouble(next());
    }

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