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Open Ural FU Personal Contest 2012

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H. The Robot on the Line

Time limit: 1.0 second
Memory limit: 64 MB
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
To submit the solution for this problem go to the Problem set: 1948. The Robot on the Line