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Function to detect presence of a variable in expression

I would like to have a function

            k = CountMeIn[expr,var]

that returns the number of times var appears in expr, eg.
CountMeIn[(1/x)^x,x]  returns 2. var could be a list, in which case
k would be a conforming list: k = CountMeIn[(2/x)^(x*w^4*z),{x,y,w,z}]
should return {2,0,1,1}.  expr is never a list.

Tried to use Position for this, but the behavior is finicky:
Position[1/x,x] returns {{1,1}} but Position[x,x] or Position[1*x,x]
returns {{}}  (why?)  May be expr should be converted  to {expr}
inside the function for safety?

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