Reverse key-value in dictionary where value is an array

Question

I have a dictionary with values as list of items as shown below :-

{
    key1: ['value1', 'value2', 'value3'],
    key2: ['value2', 'value3'],
    key3: ['value1', 'value2']
}

What I want is to reverse the key-value pair in such a way that, the keys will be now shown in a list format for each value according to its occurrence as shown below :-

{
    value1: ['key1', 'key3'],
    value2: ['key1', 'key2', 'key3'],
    value3: ['key1', 'key2']
}

I know with few iterations using for-loop and if-conditions I can do this, but I was wondering if there is any other optimized way like some built in python tools or something like that to achieve this. Any help would be highly appreciated.