There is a particle at point $$$X = 1$$$ on an infinite number line with a charge value of $$$Y$$$. When interacting with the line, it gains unusual properties: by absorbing energy, this particle releases enough kinetic energy to move $$$\gcd(X,Y)$$$ steps along the number line, where $$$\gcd(X,Y)$$$ is the greatest common divisor of $$$X$$$ and $$$Y$$$. That is, with each procedure, the particle moves from position $$$X$$$ to position $$$X + \gcd(X,Y)$$$.

Scientists need to energize the particle $$$K$$$ times in order to discover new properties about it; however, they need to predict at which point the particle will stop after these procedures so that they can reuse it in future studies.

Therefore, help determine what the final position $$$X$$$ will be after the $$$K$$$ processes.