# Finding Inverse in modulus m

I've been learning the Euclidean algorithm and came across this simple problem.

$101^{-1} (mod 203)$

So I attempted it as such:

$203 = 101(2) + 1$

So we got a gcd of 1, we can stop and do:

$1 = 203 - 101(2)$

And since it's mod 203, we have 101(2)

So shouldn't the answer be $2$? My textbook says it's $201$, help would be much appreciated, as this is confusing as ever.

Thanks.