A9773 | Tavas and Karafs

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 $n$ ( $1<=A,B<=10^{6}$ , $1<=n<=10^{5}$ ).

Next $n$ lines contain information about queries. $i$ -th line contains integers $l,t,m$ ( $1<=l,t,m<=10^{6}$ ) for $i$ -th query.

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