Else Statement Not Working

[SenkouSimmer]

This is homework, but I'm not asking anyone to do my homework for me. My professor isn't helping me with anything and I've been stuck on this one question for the past 6 hours. Here's what the questions is:
3. Write a program that lets the user type in the name of a file. Attempt to open the supplied file for read access. If the file exists, you can print out a confirmation message. If the file doesn't exist, you should tell the user that the file cannot be found.

Hint: use a try/except block to do this (don't just use a series of "if" statements - we want this program to be as "generic" as possible).

You will not get credit for this part of the program if you write something like the following to identify valid data files:

filename = input("Enter a filename: ")

if filename == "class1":
# open class1.txt
elif filename == "class2":
# open class2.txt
else:
print ("Sorry, I can't find this filename")

Here's the sample of the program you will use to test this problem:

Enter a class file to grade (i.e. class1 for class1.txt): foobar
File cannot be found.

Enter a class file to grade (i.e. class1 for class1.txt): class1
Successfully opened class1.txt

And here's what I've written as my code:

def inputfilename():
    filename = input("Filename (with extension): ")
    if filename == "class1.txt" or "class2.txt":
        openfile = open(filename, "r")
        contents = openfile.read()
        print(contents)
        contents = openfile.close()

    else:
        print("File cannot be found")

inputfilename()
inputfilename()

Whenever I type in "class1.txt" or "class2.txt", it works perfectly fine, returning the contents of both files. Whenever I type in "foobar", or anything besides "class1.txt" or "class2.txt", it returns this:
Traceback (most recent call last):
File "C:\Users\Gary\Desktop\School\Assignment Leftovers\A5\trash.py", line 12, in <module>
inputfilename()
File "C:\Users\Gary\Desktop\School\Assignment Leftovers\A5\trash.py", line 4, in inputfilename
openfile = open(filename, "r")
FileNotFoundError: [Errno 2] No such file or directory: 'foobar'

It should be returning "File cannot be found.", but it appears the "else" statement isn't properly working.

Does anyone know what I'm doing wrong? Please help soon, my assignment is due 7/21 at midnight (EST).
My code is properly spaced, but I don't know how to properly use this site, so it won't let me add spacing, sorry.