There is a quick and easy way to work out the Extended Euclidean Algorithm with pen and paper.

It involving creating a grid like this:

--+--+--+--+--+--+- ... -+----
Q:| 1| 0|Q_{O}|Q_{1}|Q_{2}| ... |
--+--+--+--+--+--+- ... -+----
P:| 0| 1|P_{0}|P_{1}|P_{2}| ... |
--+--+--+--+--+--+- ... -+----
q:| | |q_{o}|q_{1}|q_{2}| ... |q_{n}|
--+--+--+--+--+--+- ... -+----
r:| | a| b|r_{0}|r_{1}| ... |r_{n}|
--+--+--+--+--+--+- ... -+----
r:| |r_{0}|r_{1}|r_{2}|r_{3}| ...
--+--+--+--+--+--+- ... -+----

Where a and b correspond to a and b on Xamot's wu, ri is the remainder of r_{i-2}/r_{i-1} (consider a and b r_{-2} and r_{-1}), and q_{i} the quotient of the same division.

Now the Q and P rows correspond roughly to the x's and y's in Xamot's wu. The calculation for them is as follows:

P_{i}=q_{i}*P_{i-1}+P_{i-2}

Q_{i}=q_{i}*Q_{i-1}+Q_{i-2}

The way to proceed is as follows, we usually perform the simple Euclid's Algorithm first:

--+--+--+--+--+--+--+
q:| | | 1| 1| 2| |
--+--+--+--+--+--+--+
r:| |12| 7| 5| 2| 1|
--+--+--+--+--+--+--+
r:| | 5| 2| 1| | |
--+--+--+--+--+--+--+

Then we proceed with Q_{i}'s and P_{i}'s

--+--+--+--+--+--+--+
Q | 1| 0| 1| 1| 3|
--+--+--+--+--+--+--+
P | 0| 1| 1| 2| 5|
--+--+--+--+--+--+--+
q:| | | 1| 1| 2| |
--+--+--+--+--+--+--+
r:| |12| 7| 5| 2| 1|
--+--+--+--+--+--+--+
r:| | 5| 2| 1| | |
--+--+--+--+--+--+--+

So the final Q's and P's are 3 and 5, yielding the Bezout's Identity:

3*12+(-5)*7=1 (signs for Q_{i} and P_{i} alternate, one is positive for even i's and negative for odd; and the other is the opposite)

Notice that calculating P_{i} and Q_{i} is really quick, it involves looking up their previous values and q_{i} just below.

As usual, furher help is granted by msg'ing me ;-)