Robotics is very popular on the planet T4-F7 of star system of Tau
Ceti. Professor Bobov has recently demonstrated his new development—an
autonomous robot which can move in one dimension. The robot’s program
receives a real number x as input, which specifies the robot’s behavior in the
future completely. At the first second the robot covers distance
f(x) = ax2 + bx + c (if f(x) is positive, it moves to
the right, and if it is negative, the robot moves to the left). During the
next second the robot covers distance f(x + 1), during the third second
it covers distance f(x + 2) and so on.
For the presentation, professor Bobov wants to make sure that the robot
will come back to the initial position in exactly k seconds after start
of its program. So there is a question if any suitable x exists.
It may simply turn out that for any input data the robot
can’t come back to the initial point in k seconds. Help professor Bobov
finding the minimum k which allows this to happen.
The first line contains an integer t (1 ≤ t ≤ 1 000) that is the
number of tests. Each of the next t lines contains another test, i.e.,
integers a, b, c specifying the behavior of the robot. Numbers a,
b, c are less than 109 by absolute value. Number a is positive.
For every test, output the minimal positive integer k for which there is no
parameter x getting the robot back to the initial position in k seconds. If there
is no such k or it is larger than 1018, output “Infinity”.
1 -2 1
1 1 -6
Problem Author: Andrey Demidov
Problem Source: Open Ural FU Personal Contest 2012