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.util.*;
import java.io.*;
public class C {

    public static void main(String[] args) throws FileNotFoundException {
        new C().solve();
    }

    public void solve() throws FileNotFoundException {
        Scanner in = new Scanner(System.in);
        int a = in.nextInt();
        int b = in.nextInt();
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            int l = in.nextInt();
            int t = in.nextInt();
            int m = in.nextInt();

            if (calc(l, a, b) > 1L * t) {
                System.out.println(-1);
                continue;
            }

            int lo = l;
            int hi = (t - a) / b + 2;
            while (lo < hi) {
                int mid = lo + (hi - lo + 1) / 2;
                if (calc(mid, a, b) <= t * 1L && get(a, b, l, mid) <= 1L * m * t)
                    lo = mid;
                else
                    hi = mid - 1;
            }
            System.out.println(lo);
        }
    }

    public long calc(int i, int a, int b) {
        return 1L * a + (i - 1) * 1L * b;
    }

    public long get(int a, int b, int l, int r) {
        long res = 1L * a * (r - l + 1);
        long rr = r * 1L * (r - 1);
        long ll = (l - 2) * 1L * (l - 1);
        rr /= 2;
        ll /= 2;
        res += (rr - ll) * b;
        return res; 
    }
}