Extended Euclidean Algorithm

Hi all, ok so below is an example of the Extended Euclidean Algorithm, and i understand the first part perfectly to find the g.c.d.

701 − 2 × 322 = 57,

322 − 5 × 57 = 37,

57 − 37 = 20,

37 − 20 = 17,

20 − 17 = 3,

17 − 5 × 3 = 2,

3 − 2 = 1,

and

1 = 3 − 2

= 6 × 3 − 17

= 6 × 20 − 7 × 17

= 13 × 20 − 7 × 37

= 13 × 57 − 20 × 37

= 113 × 57 − 20 × 322

= 113 × 701 − 246 × 322.

Now on the second part, it is finding the equation of ax +by = 1, which i am generally having to find so i can compute the inverse of a(modb). They have managed to do this in 7 steps. It always takes me like more than twice as many in a really longwinded fashion. Has the example below missed out some steps for the sake of conciseness? I just dont understand how they are doing what they are doing.

For example I would have said

1= 3- 2

1 = (20-17) - (17 - (5x3))

1 = ((57-37) - (37-20)) - ((37-20) - 5(20-17))

etc.

Which is obviously far more longwinded, but equally as methodical. I want to know how to do this more concisely so in an exam it would be far less confusing and time consuming.

Thank you!