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 issi?=?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 thatl?≤?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.