Planet Ataraxia is known for its education centers. The people
who are expected to take high social positions in future are brought up in conditions of
continuous training and supervision from the early age. Each education
center is a small town with all the necessary utilities. During the construction of a
center, a square area is chosen which is divided into equal sections each sized
100 × 100 meters. In each of these sections they build one
building, which would become residential or academic. The outer perimeter
of the center is fenced.
After a successful military operation in the Andromeda nebula the active
colonization of habitable planets has started. The need for people
able to take command and lead people to the new worlds has increased.
Therefore, two new education centers should be built on Ataraxia.
Discussion about the details of the project in the local
administration is already underway for many days. During this time it was decided that
the first center will consist of a2 sections and that the second
one will consist of no more than n2 sections. The situation is
complicated because, according to requirements of the antimonopoly
legislation, construction works must be performed by at least two different
companies, each of them must build an equal number of buildings and an
equal number of 100-meters segments of the fence.
You are responsible for resupplying the administration office. You understand
that while they are discussing the pros and cons of each possible size of the
second center a lot of buns and coffee will be consumed, and it's time to buy
So you'd like to know how many different sizes of the second center will
meet the requirements of antimonopoly legislation and, therefore, will be
fully considered by the administration.
The only line contains integers a and n (1 ≤ a ≤ 1012; 1 ≤ n ≤ 1018).
Output an amount of different sizes of the second center meeting the requirements of antimonopoly legislation.
In this example it is possible to build the second center sized 3 ×
3 or 6 × 6, delegating the construction to three different
companies, or to build it sized 1 × 1 or 5 × 5, delegating
the construction to two different companies.
Problem Author: Ivan Burmistrov
Problem Source: Ural Championship 2012