You can't save the padding.
But you can save the carpet.
Thing is, you have to dry it quickly.
Mold needs moisture to survive.
No moisture, no mold.
You have to pull out the carpet.
Then remove and dispose of the padding.
Then bring the carpet back in and lay it out, securing it to the carpet strips with a staple gun.
Leave a small opening at a doorway or something so you can stick a carpet fan, that you can rent from Home Depot, in under the carpet and turn it on.
The whole carpet should rise like a big lava bubble.
Watch so the staples don't come out because it'll start flapping and unraveling.
Let it dry like this for a day or so till it and the floor and baseboards are completely dry.
Then remove the staples, pull the dry carpet out again, install the new padding, and re-stretch the carpet.
I know it sounds like a lot of work, but it's the only way to save the carpet from mold.
I've repaired lots of water damage..

I would toss it all -sorry– even a professional cleaner will not be able to **** the water out of the padding. Until you are totally certain you have solved the water problem—install some cheap buck a foot ceramic 12by12s from depot and use area rugs that you can toss. You really need to cure the disease not the symptoms and find out why you got water before you re-install wall to wall carpeting down their or risk this happening again.