Cheapest way from Fukuoka to Tokyo

This may have been answered but I am having a tough time figuring it out. What is the least expensive way to get from Kukuoka to Tokyo, if time isn't an issue? Thanks!

It is answered here:
http://www.japan-guide.com/e/e4802.html

Night bus sponsered by travel agency is cheapest.
(around JYE10000 oneway)
I will show you 2popular company's web site.( only Japanese site)

http://travel.willer.co.jp/route-list/kyusyu.html

http://www.sunshinetour.co.jp/bus/index.html

on foot ?

You could utilize the Seishun 18 Kippu, or Youth 18 ticket for 11,500 yen with a 5-day validity. You need to travel on local and rapid trains all the way. A one-day portion is 2,300 yen.

http://www.jreast.co.jp/e/pass/seishun18.html
http://tinyurl.com/6kp6pg

e.g. Hakata 4:50am--(3 changes en route)--13:07 Okayama 13:24--(Shinkansen Nozomi, which costs 3,130 yen additionally.)--13:45 Himeji 13:57--(5 changes en route)--23:46 Tokyo

Total cost: 5,430 yen ( used Shinkansen en route, otherwise you can't reach Tokyo in a day.)

Having explained that, you might fly with Skymark on a cheap fare by booking as early as possible. It's much more realistic.
http://www.skymark.co.jp/en/index.html