Problem:
Score : 300 points

Problem Statement

We will play a one-player game using a number line and N pieces.

First, we place each of these pieces at some integer coordinate.

Here, multiple pieces can be placed at the same coordinate.

Our objective is to visit all of the M coordinates X_1, X_2, ..., X_M with these pieces, by repeating the following move:

Move: Choose a piece and let x be its coordinate. Put that piece at coordinate x+1 or x-1.

Note that the coordinates where we initially place the pieces are already regarded as visited.

Find the minimum number of moves required to achieve the objective.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq M \leq 10^5

-10^5 \leq X_i \leq 10^5

X_1, X_2, ..., X_M are all different.

Input

Input is given from Standard Input in the following format:

N M
X_1 X_2 ... X_M

Output

Find the minimum number of moves required to achieve the objective.

Sample Input 1

2 5
10 12 1 2 14

Sample Output 1

5

The objective can be achieved in five moves as follows, and this is the minimum number of moves required.

Initially, put the two pieces at coordinates 1 and 10.

Move the piece at coordinate 1 to 2.

Move the piece at coordinate 10 to 11.

Move the piece at coordinate 11 to 12.

Move the piece at coordinate 12 to 13.

Move the piece at coordinate 13 to 14.

Sample Input 2

3 7
-10 -3 0 9 -100 2 17

Sample Output 2

19

Sample Input 3

100 1
-100000

Sample Output 3

0

Solution in Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program name
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int32):: n,m,i
    integer(int32), allocatable:: x(:),dx(:)

    read*, n,m
    if (n >= m) then
        print'(i0)', 0
        stop
    end if
    allocate(x(m))
    read*, x(:)
    allocate(dx(m-1))
    call merge_sort(x,1,m)
    do i=1,m-1
        dx(i) = x(i+1)-x(i)
    end do
    call merge_sort(dx,1,m-1)
    print'(i0)', sum(dx(1:m-n))

contains
recursive subroutine merge_sort(ar, fst, lst)
    integer(int32),intent(inout):: ar(:)
    integer(int32),intent(in):: fst,lst
    integer(int32):: mdl

    if (lst-fst < 2) then
        if (ar(fst) > ar(lst)) call swap(ar(fst),ar(lst))
        return
    end if

    mdl = (fst+lst)/2
    call merge_sort(ar, fst, mdl)
    call merge_sort(ar, mdl+1, lst)
    call merge_(ar, fst, mdl, lst)
end subroutine

subroutine merge_(ar, fst, mdl, lst)
    integer(int32),intent(inout):: ar(:)
    integer(int32),intent(in):: fst, mdl, lst
    integer(int32),allocatable:: tmp(:)
    integer(int32):: li, ri, ti

    allocate(tmp(lst-fst+1))

    li=fst
    ri=mdl+1   
    ti=1

    do while (li <= mdl .and. ri <= lst)
        if (ar(li) <= ar(ri)) then
            tmp(ti) = ar(li)
            li=li+1
        else
            tmp(ti) = ar(ri)
            ri=ri+1
        end if
        ti=ti+1
    end do

    if (li <= mdl) then
        tmp(ti:) = ar(li:mdl)
    else
        tmp(ti:) = ar(ri:lst)
    end if

    ar(fst:lst) = tmp(:)
    deallocate(tmp)
end subroutine

subroutine swap(x,y)
    integer(int32),intent(inout):: x,y
    integer(int32):: tmp
    tmp = x
    x = y
    y = tmp
end subroutine
end program name