Would this adapter work for my laptop?

I have a Gateway laptop. On the back it says:
Model No.: W3501
Input: 19v = 3.42A

And I'm looking at a adapter that is a universal mode-switching power supply, with an adjustable output DC voltage of 15V-20V/4.5A max 22-24V /4A max.

I don't know much about this. Please help me out.
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