Rund was busy this weekend preparing her computer graphics project, so she gave Bitar the following task to complete:

Given an array $a$ of $n$ integers, you have to move the elements in the array to $k$ non-empty arrays (each array has a sub-sequence from the main array) such that you maximize the result of ${\sum_{i = 1}^k mex(array[i])}$.  

The MEX (minimum excluded) of an array is the smallest non-negative integer that does not belong to the array.

For example: the MEX of [2,2,1] is 0 , the MEX of [1,2,0] is 3.

Check the Note for further explanation if needed.

The first line contains two integers $n$ , $k$ where ($1 \le k \le n \le 100000$).

The second line contains n integers $a_1 , $$a_2 , .... , $$a_n$ ($0 \le a_i \le n$).

Print a single integer , the maximum possible value of ${\sum_{i = 1}^k mex(array[i])}$.

One of the possible partitions for the first case : [1 , 0] , [2 , 5 , 1 , 0].  

The MEX for the first array is 2 , and the MEX for the second array is 3, so the answer is 2 + 3 = 5.