$($Method $2)$

$$ Take the scores of n students as input, sort them, and then

divide them into k groups.

$$ Assume that lower group numbers correspond to higher scores.

$$ It would be ideal if the scores of students within each group were

similar.

$$ Therefore, calculate the variance of student scores in each group, and

aim to minimize the sum of these variances across all groups.

$$ However, each group must have at least one student, and the variance

of a group with only one student is considered to be $0.$

Input

$$ Take input from standard input.

$$ The first line contains n and k$.$

$$ The next line contains the scores of n students in ascending order of

enrollment numbers.

$$ Here, n is a number greater than or equal to k$.$

$$ Each score can range from $0$ to $1,000,$ and ties are possible.

$$ Surprisingly, n can be as large as $10^4.$

$$ k is a positive integer less than or equal to $12.($Note: depending on the

school, each grade $($A$,$ B$,$ C$,$ D$)$ may be divided into $2$ or $3$ categories$)$

Output

$$ Print to standard output and write to files simultaneously.

$$ Print the $($minimum$)$ sum of variances in Method $2$ on the second line

of standard output $($rounded to three decimal places$).$

$$ Write the groups from Method $2$ to a file $($filename: Partition$2.$txt$).$

The first line of the file corresponds to Group $1,$ and the kth line

corresponds to Group k$.$ Each line lists "student number $($student

score$)"$ in ascending order of student numbers

Example

Input $($standard$/$console input$)$

$153$

$50851035451575802530556065705$

$$ Output $($standard$/$console output$)$

$197\mathrm{.}917$

Output $($filename: Partition$2.$txt$)$

$2(85)7(75)8(80)13(65)14(70)$

$1(50)5(45)11(55)12(60)$

$3(10)4(35)6(15)9(25)10(30)15(5)$