recursive function: use a global or pass a parameter?

[Tim]

I have this type of situation and wonder if I should use a global variable outside the recursive function instead of passing the updated parameter through. 

I want to get a union of all the values that any 'things' key may have, even in a nested dictionary (and I do not know beforehand how deep the nesting might go):

d = {'things':1, 'two':{'things':2}}

def walk(obj, res):
    if not hasattr(obj, 'keys'):
        return set(), set()
    
    if 'things' in obj:
        res.add(obj['things'])
        
    for k in obj:
        walk(obj[k], res)
        
    return res

walk(d, set()) # returns {1, 2}

Is it better to use a global to keep track of the values or does it even matter?

thanks,
--Tim