Mongodb Or query with two arrays

I am trying to perform an or query in MongoDB.

I have two array

firstNames = ['John', 'Tim','Joey']
lastNames = ['Alex', 'Smith', 'Mac']

I want to perform a query like

{$or: [{firstName: 'John', lastName: 'Alex'}, {firstName: 'John', lastName: 'Smith'}, {firstName: 'John', lastName: 'Mac'}, {firstName: 'Tim', lastName: 'Alex'} ... ]}

I tried

1.

Users.find({firstName: {$in: firstNames}, lastName: {$in: lastNames} })

Users.find({$or:[{firstName: {$in: firstNames}}, {lastName: {$in: lastNames} }]})

but this is wrong I guess. Can someone provide a better solution to this?