update key, values in a dictionary

Question

I have a dictionary with lists as values:

foo = {5:[1,2,3]}

I want to add 1 to key as well as values and for that, I did this :

bar = {}
for k,v in a.items():
    z = []
    for i in v:
        z.append(i+1)
    bar[k+1] = z

Is there a better way to do this and does that method save runtime?

Excpected Result:

bar = {6: [2, 3, 4]}