In the movie "Thoroughly Modern Millie" Julie Andrews and Mary Tyler Moore danced in an elevator. What is the name of the song they danced to?

From IMDb:
"Stumbling"
(uncredited)
Written by Zez Confrey
Danced by Julie Andrews and Mary Tyler Moore in the elevator

Here's a recording of it: https://www.youtube.com/watch?v=nDGEZEryjP4

Here it is as part of the Overture to "Thoroughly Modern Millie":
https://www.youtube.com/watch?v=CfiMOV-AkG8