Is it Possible to Beat New Super Mario Bros. U Without Touching a Single Coin?

Can New Super Mario Bros. U be beaten without ever touching a single coin? New Super Mario Bros U is one of my favorite Super Mario games, I replay it every couple of months. But I usually not only try to beat NSMBU, but I also challenge myself to play through the game in a certain way, so that it stays fun, and challenging. So for my latest playthrough I thought it would be fun to try to collect the least amount of coins possible, while still beating New Super Mario Bros. U.