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.

<image>

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.*;

public class Solution
{
       public static void main(String []args)
       {
              Scanner sc = new Scanner(System.in);
              long a = sc.nextLong();
              long b = sc.nextLong();
              int q = sc.nextInt();
              while(q-- > 0)
              {
                     int l = sc.nextInt();
                     int t = sc.nextInt();
                     int m = sc.nextInt();
                     
                     long ll = 1;
                     long rr = 100000000L;
                     while(ll <= rr)
                     {
                        long mid = (ll+rr)/2;
                        long al =  a + (long)(l-1)*b;
                       
                        
                        long sum = mid*(2*al + (mid-1)*b)/2;
                        if(sum <= (long)m*t  && al + (mid-1)*b <= t)
                        ll = mid+1;
                        
                        else
                        rr = mid-1;
                     }
                     if(rr != 0)
                     System.out.println(l+rr-1);
                     
                     else
                     System.out.println("-1");
              }
       }
}