From Wikipedia:

In modular arithmetic,   the modular multiplicative inverse of an integer    a    modulo    m    is an integer    x    such that





a

x
≡
1


(
mod

m
)

.


{\displaystyle a\,x\equiv 1{\pmod {m}}.}


Or in other words, such that:





∃
k
∈

Z

,

a

x
=
1
+
k

m


{\displaystyle \exists k\in \mathbb {Z} ,\qquad a\,x=1+k\,m}


It can be shown that such an inverse exists   if and only if    a    and    m    are coprime,   but we will ignore this for this task.



Task

Either by implementing the algorithm, by using a dedicated library or by using a built-in function in
your language,   compute the modular inverse of   42 modulo 2017.




П1	П2	<->	П0	0	П5	1	П6	ИП1	1
-	x=0	14	С/П	ИП0	1	-	/-/	x<0	50
ИП0	ИП1	/	[x]	П4	ИП1	П3	ИП0	^	ИП1
/	[x]	ИП1	*	-	П1	ИП3	П0	ИП5	П3
ИП6	ИП4	ИП5	*	-	П5	ИП3	П6	БП	14
ИП6	x<0	55	ИП2	+	С/П