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 static java.lang.Math.*;
import java.io.*;

public class A {
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer stok = new StringTokenizer(in.readLine());
        long A = Integer.valueOf(stok.nextToken());
        long B = Integer.valueOf(stok.nextToken());
        long N = Integer.valueOf(stok.nextToken());
        StringBuffer ans = new StringBuffer("");
        for (int i = 0; i < N; i++) {
            stok = new StringTokenizer(in.readLine());
            long l = Integer.valueOf(stok.nextToken());
            long t = Integer.valueOf(stok.nextToken());
            long m = Integer.valueOf(stok.nextToken());

            if (score(A, B, l, l, m) > t) {
                ans.append("-1\n");
                continue;
            }

            long max = l;
            while (true) {
                if (score(A, B, l, max, m) <= t) {
                    max *= 2;
                } else {
                    break;
                }
            }
            long low = l;
            long high = max;
            while (low  + 1 < high) {
                long mid  = (low + high) / 2;
                if (score(A, B, l, mid, m) <= t) {
                    low = mid;
                } else {
                    high = mid;
                }
            }
            ans.append(low+"\n");
        }
        System.out.print(ans);
    }

    static long score(long A, long B, long l, long r, long m) {
        long n = r - l + 1;
        long total = (A + (l - 1) * B) * n;
        total += (n * (n - 1) / 2) * B;
        return max(A + (r - 1) * B, (total + m - 1) / m);
    }
}
