Tokyo to Kamikochi, mountain hut / camping?

Hello,

I am looking to travel to/from Tokyo to Kamikochi to do 5-6 days of hiking in the mountains. I am looking for the cheapest and/or fastest way to get from Tokyp to Kamikochi.

My main goal is do as much hiking as possible, covering as much ground as I can. Does anyone have any suggestions for a hiking loop that would be 5-6 days long, 6-8 hours of hiking each day?

Additionally, I am contemplating brining a sleeping bag and bivy sack because it seems like the mountain huts are quite expensive. Does anyone have any info on how cold it gets at night and if I need a permit?

Thank you!

Maybe, I think the cheapest and quickest method is by directly bus called SAWAYAKA-SHINSHU-GO between Shinjuku and Kamikochi.
★Timetable:From/To
The west exit of the SHinjuku station(Keio-high-speed　bus terminal) and Kamikochi bus terminal.07:20/12：02 or 22:30/05：30
Return will be:15：00/19：42 or 16:15/20:57
6,200yen/one way(standard seat/off-season )
7,400yen/one way(standard seat/on-season)
Advanced reservations required!
https://www.highwaybus.com/html/gp/foreign/en/access/index.html
About Weather and temperature etc.
http://www.kamikochi.or.jp/english/
http://www.japan-guide.com/e/e6040.html
Have a nice trip!