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 Karafs {
    public static void main(String[]args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int A = Integer.parseInt(st.nextToken());
        int B = Integer.parseInt(st.nextToken());
        int q = Integer.parseInt(st.nextToken());

        long [] sum = new long[1000001];
        for (int i = 1; i < sum.length; i++) {
            sum[i] = sum[i-1] + A+(i-1)*(long)B;
        }

        for (int i = 0; i < q; i++) {
            st = new StringTokenizer(br.readLine());
            int l = Integer.parseInt(st.nextToken());
            int t = Integer.parseInt(st.nextToken());
            int m = Integer.parseInt(st.nextToken());

            if (sum[l]-sum[l-1] > t) {
                System.out.println(-1);
                continue;
            }

            int r = (t-A)/B + 1;
            
            if (m >= r-l+1) {
                System.out.println(r);
                continue;
            }
            
            int min = l;
            int max = r;
            while (min < max) {
                int mid = (max+min+1)/2;
                if (sum[mid] - sum[l-1] - t*(long)m > 0) {
                    max = mid-1;
                } else {
                    min = mid;
                }
            }
            System.out.println(min);
        }
    }
}
