gcd (42,660 )

660 = 41*16 + 4

41 = 4 * 10 + 1

4 = 1 * 4 + 0

so gcd ( 42, 660 ) = 1

How do express it as linear combination of 41 and 660. I know i work backward....and i get this far and i get stuck..

1 = 41-4*10

1 = 41-(660-41*16)*10

After that...i have no idea what to. I have been reading the examples and problems people have done on this site but i just can't figure out where their numbers are coming from. Any help would be appreciated...Thank you