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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad.ST
import Data.Array.ST
import Control.Monad
import Data.Array
import Data.List

main = do
  (n:k:xx) <- map read . words <$> getLine 
  xs <- map read . words <$> getLine
  putStrLn . show $ solve n k xs

solve :: Int -> Int -> [Int] -> Int
solve n k xs = sum . take (n-k) . sort . elems $ runSTArray $ calcInST n xs


calcInST :: Int -> [Int] -> ST s (STArray s Int Int)
calcInST n xs = do
  arr <- newArray (1,n) 0
  forM_ xs $ \x -> do
    v <- readArray arr x 
    writeArray arr x (v+1)
  return arr