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.*;

public class Solution {

    static long ans=-1;
    static long sent=(long)Math.pow(10,12);
    static void BinarySearch(int a,int b,long low, long high, long x,int left,int m,long vleft)
    {
        if(low > high){
            return ;
        }
        long mid = (low+high)/2;
        long val=a+(mid-1)*b;
        long n=(mid-left+1);
        long sum=(n*(2*vleft+(n-1)*b))/2;
        if(x>=val && sum<=x*m){
            ans=mid;
            BinarySearch(a,b,mid+1,high,x,left,m,vleft);
        }
        else
            BinarySearch(a,b,low,mid-1,x,left,m,vleft);
    }

    public static void main(String args[]){
        Scanner in=new Scanner(System.in);
        int a=in.nextInt(),b=in.nextInt(),n=in.nextInt();
        for(int i=0;i<n;i++){
            int l=in.nextInt(),t=in.nextInt(),m=in.nextInt();
            long vleft=a+(l-1)*b;
            if(t<vleft){
                System.out.println("-1");
            }
            else{
                BinarySearch(a,b,l,sent,t,l,m,vleft);
                System.out.println(ans);
                ans=-1;
            }
        }
        in.close();
    }
}
