I'm trying to make sense out of this table.
I understand the $k,j,q$, and $r$ part but I don't understand how they get the $x$ and the $Y$. Any and all help is much appreciated!
2026-03-28 07:57:01.1774684621
Euclid's Extended GCD Inverse
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At each step (going upwards), the algorithm computes a vector (x,y). The vector obtained at the previous step is denoted $(x',y)'$, $q$ is the current quotient, and the relation between $(x,y)$ and $(x',y')$ is given by $$x=y'-qx', \quad y=x'.$$ For instance, having obtained $(7,-3)$ (3rd line from bottom) the next vector will be $x=-3-6\cdot 7-45,\quad y=7$.