Henry writes Chinese essays every day to prepare for the upcoming HKDSE examination. He has written $N$ essays so far, the $i$-th essay consists of $A_i$ characters.

Now, Henry wants to post $K$ of his $N$ essays to the popular Android app Fascinating Compositions. Due to aesthetic considerations, Henry wants the $K$ essays he post to have the same number of characters. Therefore, Henry will edit his essays to meet this requirement.

In one operation, Henry can add one character to any essay. What is the minimum number of operations for Henry to meet the requirement?

Input

The first line of input contains two integers $N, K$.
The second line of input contains $N$ integers $A_1, A_2, \cdots, A_N$.

Output

Output an integer: the minimum number of operations for Henry to have $K$ essays with the same number of characters.

Constraints

For all subtasks, $1 \le K \le N \le 10^5, 1 \le A_i \le 10^9$
Subtask 1 (30%): $1 \le N \le 2000$
Subtask 2 (70%): No additional constraints