Problem:
Score : 300 points

Problem Statement

In some other world, today is Christmas Eve.

There are N trees planted in Mr. Takaha's garden. The height of the i-th tree (1 \leq i \leq N) is h_i meters.

He decides to choose K trees from these trees and decorate them with electric lights. To make the scenery more beautiful, the heights of the decorated trees should be as close to each other as possible.

More specifically, let the height of the tallest decorated tree be h_{max} meters, and the height of the shortest decorated tree be h_{min} meters. The smaller the value h_{max} - h_{min} is, the better. What is the minimum possible value of h_{max} - h_{min}?

Constraints

2 \leq K < N \leq 10^5

1 \leq h_i \leq 10^9

h_i is an integer.

Input

Input is given from Standard Input in the following format:

N K
h_1
h_2
:
h_N

Output

Print the minimum possible value of h_{max} - h_{min}.

Sample Input 1

5 3
10
15
11
14
12

Sample Output 1

2

If we decorate the first, third and fifth trees, h_{max} = 12, h_{min} = 10 so h_{max} - h_{min} = 2. This is optimal.

Sample Input 2

5 3
5
7
5
7
7

Sample Output 2

0

If we decorate the second, fourth and fifth trees, h_{max} = 7, h_{min} = 7 so h_{max} - h_{min} = 0. This is optimal.

There are not too many trees in these sample inputs, but note that there can be at most one hundred thousand trees (we just can't put a sample with a hundred thousand lines here).

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

program atcoder_abc115c_sort
    implicit none
    integer(8) :: n,k,i,ans=10000000000_8
    integer(8),allocatable,dimension(:) :: a,ind
    read*,n,k
    allocate( a(n) )
    allocate( ind(n) )
    read(*,*)(a(i),i=1,n)
    do i=1,n
        ind(i) = i;
    end do
    call sort(a,ind)
    do i=1,n-k+1
        ans = min(ans,a(i+k-1)-a(i))
    enddo
    write(*,'(I0)')ans


  !----------------------functions--------------------------
  contains
  recursive subroutine mergesort(a, p, r, b,ia,ib)
  integer(8) a(:), b(:),ia(:),ib(:)
  integer(8) p, r
  integer(8) q
  if (p < r) then
    q = (p+r)/2
    call mergesort(a, p, q, b,ia,ib)
    call mergesort(a, q+1, r, b,ia,ib)
    call merge(a, p, q, r, b, ia,ib)
  end if
  end subroutine mergesort
  subroutine merge(a, p, q, r, b, ia,ib)
    integer(8) a(:), b(:),ia(:),ib(:)
    integer(8) p, r, q, i, j, k
    integer(8) t,ti
    k = p;   i = p;   j = q+1
    do
      if (.not. (k <= r)) exit
      if (j > r) then
        t = a(i); ti = ia(i); i = i+1
      else if (i > q) then
        t = a(j); ti = ia(j); j = j+1
        
      else if (a(i) <= a(j)) then
        t = a(i); ti = ia(i); i = i+1
      else
        t = a(j); ti = ia(j); j = j+1
      end if
      b(k) = t; ib(k) = ti; k = k+1

    end do
    do i = p, r
      a(i) = b(i)
      ia(i) = ib(i)
    end do
  end subroutine merge
  subroutine sort(a,ia)
    integer(8) a(:), b(size(a)),n,ia(:),ib(size(a))
    n = size(a)
    call mergesort(a,1_8,n,b,ia,ib)
  end subroutine sort
  end program atcoder_abc115c_sort