What was the second Mario game made?

It's a pretty interesting story, actually. In Japan, the second Mario game, called "The Lost Levels" in America, was similar to the first Mario game, but was much harder. Nintendo of America believed that it wouldn't sell well due to its difficulty, so they took an obscure Japanese game called "Doki Doki Panic," replaced the characters with Mario characters, and released it as Super Mario Bros. 2 in America. So, what the second Mario game is can be disputed, but considering that "The Lost Levels" was made first, that can technically be called the second Mario game.