euclidean algorithm iteration problem So if I have a congruence of the form $ad \equiv 1 \mod m$, where $a$, $d$, $m$ are all integers and $m > a$, I should be able to find the integer $d$ satisfying the congruence using the Euclidean algorithm. 
For example, $7d \equiv 1 \mod 30$ inserted into the Euclidean algorithm gives
\begin{align*}
30 & = 4 \cdot 7 + 2\\ 
7 & = 3 \cdot 2 + 1
\end{align*}
Working backwards gives 
\begin{align*}
1 & = 7 - 3 \cdot 2\\
  & = 7 - 3(30 - 4 \cdot 7)\\
  & = 13 \cdot 7 + (-3) \cdot 30
\end{align*}
[easily seen through some rearranging]
And so obviously $d = 13$, as $13 \cdot 7 = 1 \mod 30$ as desired. 
I'm trying to execute this for $3d = 1 \mod 100$ But I always end up like this 
\begin{align*}
A & = qB + r\\ 
100 & = 33 \cdot 3 + 1\\
1 & = 3 \cdot (-33) + 100 \cdot 1
\end{align*}
$d$ should turn out to be $67$, but I can't get to it. Help is appreciated

Your answer is correct, since
$$-33\equiv 67\mod 100$$
