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.util.StringTokenizer;

public class CF299A {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer strtok;
        strtok = new StringTokenizer(in.readLine());
        long A = Integer.parseInt(strtok.nextToken());
        long B = Integer.parseInt(strtok.nextToken());
        int n = Integer.parseInt(strtok.nextToken());
        for (int i = 0; i < n; i++) {
            strtok = new StringTokenizer(in.readLine());
            int l = Integer.parseInt(strtok.nextToken());
            int t = Integer.parseInt(strtok.nextToken());
            int m = Integer.parseInt(strtok.nextToken());
            if (A + B * (l - 1) > t) {
                System.out.println(-1);
                continue;
            }
            int lo = l;
            int hi = t + 1;
            while (hi > lo) {
                int mid = lo + hi >> 1;
                long s = A * mid + B * mid * (mid - 1) / 2 - A * (l - 1)
                        - B * (l - 1) * (l - 2) / 2;
                if (A + B * (mid - 1) > t || s > t * 1L * m)
                    hi = mid;
                else
                    lo = mid + 1;
            }
            System.out.println(hi - 1);

        }
    }
}
