Can any one explain extended Euclidean algorithm using 51!/61

Not so clear after 9p mod61=60

I don't know about Euclidean Algorithm but we can solve it using Wilson's Theorem
60! mod 61 = 60(From Wilson's Theorem)
51!*52*52.......*60 mod 61 = 60
51! * -9*-8....*-1 mod 61 = 60
51!*11*8*41 mod 61 = 60
51!*11*23 mod 61 = 60
51!* 9 mod 61 = 60
Let the remainder with 51! be p
Then 9p mod 61 = 60
From this we can have p =27.
I hope it is clear.