Karafs is some kind of vegetable in shape of an 1 \times h rectangle. Tavaspolis people love Karafs and they use Karafs in almost any kind of food. Tavas, himself, is crazy about Karafs.

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) \times 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 \le 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.

The first line of input contains three integers A, B and n (1 \le A,B \le 106, 1 \le n \le 105).

Next n lines contain information about queries. i-th line contains integers l,t,m (1 \le l,t,m \le 106) for i-th query.

For each query, print its answer in a single line.