Also: modern gasoline burns MUCH slower than the 197060s and 1970s stuff did. The 4-cable carbs always ran somewhat rich below 5500 RPM, too. Add those together and you get, using stock timing and jetting, a wet cylinder that tends to hang at high idle. The K0 always has suffered from this, the K1 a little less, since about the 1990s or so.
My solution has been to attack the richness. This can be done directly by augmenting the aeration holes in both the pilot jets and the mainjet emulsifiers: I use 0.039" drills in the mainjet emulsifiers first, in all their big (0.0365") holes. Leave the 2 pair of smaller holes (0.025") as they are, they function above 5500 RPM just fine after this mod. After this, set the idle airscrews inward toward 3/4 turn, too. If it dies immediately after returning to (warm) idle after throttle snap, turn them out toward 7/8 turn. In any case, 1 turn out is too rich for the modern gas, even running Regular grade: if you are running Premium this whole idle situation is much worse. Use Regular unless touring at high speeds: then Midgrade or (above 70 MPH) Premium is OK.
In stubborn cases (usually those carbs from sandcast short-slide carbs or high-mileage K0 bikes with leaky slides where the carb bodies are somewhat worn) you can enlarge the pilot jet's air holes, too. I think the right size is 0.0275", but have to go find my carb refernce notes for that one. In any event, it is the next-size-larger drill than they are when stock. Then set the aircsrews at 7/8 turn for starters, adjust in/out slightly when fully warmed up as needed.
Both of these mods will also reduce the tendency of the K0 to foul sparkplugs. Also, if you have #120 Keihin mainjets, consider using #115 instead with modern fuels, too.