You might be able to save the vinyl if it has not started to mold. You won't know till you pull it back as the mold will start from the bottom. You will have to cut out flooring until you reach the center of a stringer and patch in a new piece. Be sure to caulk the crack along the edges. If your vinyl is not salvageable you could install some contrasting plank flooring with a transition strip between the two types of flooring.
You will have to remove all the built-in cabinets mounted on the flooring to accomplish the above repair.
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