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.




print multInv(42, 2017)
end
 
function multInv(a,b)
	b0	= b
	multInv	= 1
	if b = 1 then goto [endFun]
	while a > 1
		q	= a / b
		t	= b 
		b	= a mod b
		a	= t
		t	= x0 
		x0	= multInv - q * x0
		multInv	= int(t)
	wend
	if multInv < 0 then multInv = multInv + b0
[endFun]
end function