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 $*r*$.

Input

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.

Output

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