Please help me correct codes for running these by using the hint of the problems and fix these lines which has "FIXME...$\text{'}$ on it$.$Problem $1$:

Complete the function equiv$\_$to$(a,m,$ low, high$)$ that returns a list of all the integers $x$ in

the range low, high$]$ such that $x-=a(modm).$

EXAMPLES:

Finding all integers $-10x15$ such that $x-=3(mod5)$ :

IN: equiv$\_$to$(3,5,-10,15$

OUT : $-7,-2,3,8,13$

Finding all integers $-29x-11$ such that $x-=3(mod5)$ :

IN: equiv$\_$to$(12,15,-29,-11$

OUT: $-18$

Finding all integers $3x21$ such that $x-=-20(mod4)$ :

$IN$: $equi{v}_{t}o(-20,4,3,21)$

OUT: $[4,8,12,16,20]$

HINT:

By definition, all integers $x$ that are equivalent to a under modulo $m$ must satisfy that

$x-a=m*k,$ for some integer $k$

Hence,

$x=mk+a$

Notice that if all the $x$ values must to be in the range $[$low$,$ high$],$ then

low $mk+a$ high

What lower$-$ and upper$-$bound does this place on $k?$ How do these $k-$values allow us to find the

goal $x-$values?

def equiv$\_$to$($a$,$ m$,$ low, high$)$:

k$\_$low $=$ # FIXME: update $k_{{?}_{l}ow}$

k$\_$high $=$ #FIXME: update k$\_$high

k$\_$vals $=$ list range $,$ k$\_$high $+1$