I spent forever trying to find a YouTube video that was precisely 16m18s, and when I finally did, the video ID included periodic elements and Roman numerals that broke my earlier rules, and I gave up. Fun game though!
"00:00 / <minutes>:<seconds>" youtube
Google that, including the quotes, replace the minutes and seconds with your given time, then look through the results and find a URL which fits the password criteria.
Every result should be a video with that duration. If it isn't, check your useragent. I noticed some weirdness with that.
> site:youtube.com "00:00 / 16:18"
Or you know you could just try to work it out for yourself.