Inside the filter tool is this inscription...74/76×15.....15 stands for 15 flutes on the filter....just input 74/76×15 on your ebay search and the correct filter tool for the k series comes up....fits yamaha motorbikes too....cheapest about £8..??...ignore the ones from the states etc with massive postal costs.....picture of size inscribed in tool below.
Connected to ratchet...I only use the cup tool for removal and rely on hands for insertion
But if you have a big pair of plumbers pliers that open wide enough to grip the bottom of the filter...
I remove filters on commercial vehicles that appear welded on and it's better to apply preasure slowly and surely rather than tryng to wrench them...or it just destroys the filter and the rim still stays securely fitted..