cyclic rotation with absolute diffrence of two arrays

Example

For

nuxi $=[1,4,2,12]$ and

the output should be

solution$($mus$-1,$ nusin$)=$

$[7,13,25,25].$

$.$

Let's consider all possible cyclic $t-$shifts of

numis$1$

The $0-$shift is $1,4,2,11,$ and the sum of absolute differences with

nums $2=[10,1,8,4]$

$=|1-10|+|4-1|+|2-8|+|11-4|=9+3+6+7=25.$

The $1-$shift is $11,1,4,2,$ and the sum of absolute differences with nums $2=[10,1,8,4]$ :

$=|11-10|+|1-1|+|4-8|+|2-4|=1+0+4+2=7$

The $2-$shift is $2,11,1,4,$ and the sum of absolute differences with nums $2=[10,1,8,4]$ :

$=|2-10|+|11-1|+|1-8|+|4-4|=8+10+7+0=25$

The $3-$shift is $4,2,11,1,$ and the sum of absolute differences with nums $2=[10,1,8,4]$ :

$=|4-10|+|2-1|+|11-8|+|1-4|=6+1+3+3=13.$

The non$-$descending list of all the sums is $7,13,25,25,$ which is the answer.