dict of lambda functions in python

Question

Good evening.

I have a dict of the following type:

d = {key1: 1, key2: 2}

and I would like to define a corresponding dict of lambda functions as

functions = {key1: (lambda x: 1*x), key2: (lambda y: 2*y)}.

But somehow the following code

functions = {key: (lambda x: value*x) for key, value in d.items()}

is not yielding the desired result, as the functions for both keys are the same. Has someone an idea for a workaround?

Thanks in advance