Which game was redesigned into the international Super Mario Bros. 2?

Yume Kōjō: Doki Doki Panic was redesigned into the international Super Mario Bros. 2.

Nintendo of America wanted a sequel that would be more approachable than Super Mario Bros.: The Lost Levels, whose extreme difficulty made it a poor fit for many international players. Rather than localizing that game, Nintendo adapted the 1987 Japanese title Yume Kōjō: Doki Doki Panic for release overseas as Super Mario Bros. 2 in 1988.

The conversion replaced the original characters with Mario, Luigi, Princess Toadstool, and Toad. Their abilities were based on the corresponding characters in Doki Doki Panic: Luigi jumped higher, Princess Toadstool hovered, Toad moved quickly, and Mario provided balanced performance.

This explains why the international Super Mario Bros. 2 feels so different from the first game. Its vegetable-pulling mechanic, vertically oriented stages, and dream-world setting originated in Doki Doki Panic. In Japan, the game was later released as Super Mario USA.