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on generating combinations among a variable list of lists

Say we have [1,3,5,7], [2,3], [1,10].  I'd like to generate

  [5, ...]

The number of input lists is variable.  The example shows three lists,
but there could be only one or ten lists or any other number of lists.

I looked at itertools.  There doesn't seem to be any procedure ready for
this.  I might have to combine some of them but I'm not yet sure how.