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.




modInverse: function [a,b][
    if b = 1 -> return 1
 
    b0: b   x0: 0   x1: 1
    z: a
 
    while [z > 1][
        q: z / b        t: b
        b: z % b        z: t
        t: x0           x0: x1 - q * x0
        x1: t
    ]
    (x1 < 0) ? -> x1 + b0 
               -> x1
]
 
print modInverse 42 2017