Find integers $k$ and $l$ such that $\gcd(-5775,-651)$ can be expressed in the form $ka + bl$

Question

As the title suggests, I have to find the following:

$k$ and $l$ such that $\gcd(-5775,-651)$ can be expressed in the form $ka + bl$

Now, the main issue, I have is figuring out how the negatives play into the scenario. I did Euclid's algorithm in reverse and found that I get $71(651) - 8(5775)$. This would mean that $k = -8$ and $l = 71$ but the answers are $k = 8$ and $l = -71$. So the question is:

How do negatives factor in when finding $k$ and $l$?

Thanks a lot!

Answer 1

Note that $$71(651)-8(5775)=-71(-651)+8(-5775)$$