After coming back from trick-or-treating, Jayden now has ~N~ candies that he can eat over the next ~M~ days.

Jayden's mom allows him to eat as many candies as he wants for ~M~ days, but on the condition that he does not touch anything sweet for the rest of the year.

Jayden has a severe case of OCD (Obsessive Compulsive Disorder), and he forces himself to perfectly portion his candies, meaning that he will only eat a candy if he can eat the same amount of that brand of candy every day over the ~M~ days. In order to achieve this, he will even give out some candy to his friends if he can't portion it evenly for the next ~M~ days.

How many candies will Jayden need to give out?

Constraints

~1\le N \le 1\times 10^6~

~1\le M \le 364~

Input Specification

The first line of input will contain two space-separated integers, ~N~ and ~M~.

The next ~N~ lines of input will contain the brand of the ~i^{th}~ candy (The brand names will all be lowercase characters).

Output Specification

Output one integer, the number of candies that Jayden will need to give away.

Sample Input

10 3
kitkat
kitkat
smarties
kitkat
kitkat
aeros
snickers
smarties
aeros
aeros

Sample Output

4

Sample Output Explanation

Jayden can eat 1 aeros and 1 kitkat per day. He will have 1 kitkat, 2 smarties, and 1 snickers left over, which he can't evenly portion over 3 days, so he must give them away.