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.




MsgBox, % ModInv(42, 2017)
 
ModInv(a, b) {
	if (b = 1)
		return 1
	b0 := b, x0 := 0, x1 :=1
	while (a > 1) {
		q := a // b
		, t  := b
		, b  := Mod(a, b)
		, a  := t
		, t  := x0
		, x0 := x1 - q * x0
		, x1 := t
	}
	if (x1 < 0)
		x1 += b0
	return x1
}