Pam is intruiged by the friend groups at her school. At the beginning of the school year, there are ~N~ lone students, none of which know each other. A "join" happens when either

• 2 different lone students or
• 2 different friend groups or
• a single lone person and a friend group join together to form a single friend group.

If ~K~ such joins occur throughout the school year, how many distinct friend groups will exist at the end of the school year? (Note that a lone person is also considered as a friend group).

Constraints

~1 \le K < N \le 10^5~.

Input Specification

Two space-separated integers on one line: ~N~ (the initial number of students) and ~K~ (the number of joins that occur throughout the year).

Output Specification

One integer: the number of distinct friend groups at the end of the year.

Sample Input

3 2

Output for Sample Input

1

Explanation for Sample Case

A possible sequence of events is:

Initially, everyone is a lone student:

Person ~1~ joins with Person ~2~:

Lastly, the [~1~, ~2~] friend-group joins with Person ~3~:

Since all three of them are in the same friend group, there is ~1~ friend group that remains.