## Friend Groups

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Points: 3
Time limit: 1.0s
Memory limit: 64M

Author:
Problem type

Pam is intruiged by the friend groups at her school. At the beginning of the school year, there are 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 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).

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#### Input Specification

Two space-separated integers on one line: (the initial number of students) and (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 joins with Person :

Lastly, the [, ] friend-group joins with Person :

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