Either will do. As long as the tubers are protected from frost, they should be fine. If frost is likely to penetrate below a few inches, then I'd be inclined to lift and store, just short of dry, so they stay nice and plump for next spring.

great thank you :)

I lift mine and store in a very lightly most mixture of peat and sand - About Feb but allow them to dry out 1st I hang mine for about a week to let them get rid of any sap in the hollow cain - I bring them out and place each tuber int a box of damp compost not covering them fully and lable them put them onto my bench in the green house - once the new shoots are about 3 inches tall I pot on into a mixture of potting compost and grit - you can cut the tubers from the main stem as long as you take them with an eye still atached or they will not produce groth