I came through a problem in programming which needs Extended Euclidean Algorithm, with $a*s + b*t = \gcd(|a|,|b|)$ for $b \leq 0$ and $a \geq 0$
With the help of this post: extended-euclidean-algorithm-with-negative-numbers
I know we can just move the sign towards $t$ and just use normal Extended Euclidean Algorithm and use $(s,-t)$ as solution
However in my scenario, there is one more condition: I would like to find the minimum non-negative solution, i.e. $(s,t)$ for $s,t\geq 0$
And my question is how to find such minimum $(s,t)$?
Sorry if it sounds too obvious as I am dumb :(