Problem:
Score : 300 points

Problem Statement

Takahashi has N balls. Initially, an integer A_i is written on the i-th ball.

He would like to rewrite the integer on some balls so that there are at most K different integers written on the N balls.

Find the minimum number of balls that Takahashi needs to rewrite the integers on them.

Constraints

1 \leq K \leq N \leq 200000

1 \leq A_i \leq N

All input values are integers.

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 ... A_N

Output

Print the minimum number of balls that Takahashi needs to rewrite the integers on them.

Sample Input 1

5 2
1 1 2 2 5

Sample Output 1

1

For example, if we rewrite the integer on the fifth ball to 2, there are two different integers written on the balls: 1 and 2.
On the other hand, it is not possible to rewrite the integers on zero balls so that there are at most two different integers written on the balls, so we should print 1.

Sample Input 2

4 4
1 1 2 2

Sample Output 2

0

Already in the beginning, there are two different integers written on the balls, so we do not need to rewrite anything.

Sample Input 3

10 3
5 1 3 2 4 1 1 2 3 4

Sample Output 3

3

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

program ARC086C
    implicit none
    integer(8)::N,K,valiation,i
    integer(8)::remove=0
    integer(8)::result=0
    integer(8),allocatable,dimension(:)::A,L
    read(5,*)N,K
    allocate(A(N))
    allocate(L(N))
    valiation=N
    L=0
    read(5,*)(A(i),i=1,N)

    do i=1,N
        L(A(i))=L(A(i))+1
    end do

    L=iqsort(L)

    do i=1,N
        if(L(i)==0)then
            valiation=valiation-1
        else
            exit
        end if
    end do

    remove=valiation-K

    if(remove>0)then
        do i=1,N
            if(L(i)/=0)then
                result=result+L(i)
                remove=remove-1
            end if

            if(remove==0)then
                exit
            end if
        end do
    end if

    print'(i0)',result

contains
    recursive function iqsort(ix) result(ires)
      integer(8), allocatable :: ires(:)
      integer(8), intent(in)  :: ix(:)
      integer :: k
      if (size(ix) <= 1) then 
        ires = ix
      else  
        k = ix(size(ix) / 2)
        ires = [iqsort(pack(ix, ix < k)), pack(ix, ix == k), iqsort(pack(ix, ix > k))] 
      end if
    end function iqsort
end program ARC086C