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.

Each Karafs has a positive integer height. Tavas has an infinite 1-based sequence of Karafses. The height of the i-th Karafs is s_i=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 s_l,s_l+1,...,s_r 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≤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.

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