Convert Map<List> to List<NewType> with new java 8 streams

I need help using the java 8 streams API to convert

Map<String, List<Entry<Parameter, String>>> inputData

to

List<TestSession> testList

with the following test session

private static class TestSession {
    final String mServiceName;
    final Parameter mParam;
    final String mData;
    public TestSession(
        final String aServiceName,
        final Parameter aParameter,
        final String aData) {
        mServiceName = aServiceName;
        mParam = aParam,
        mData= aData;
    }
}

and

enum Parameter {
    Foo,
    Bar,
    Baz
}

Lets say that input data contains the following

{"ABC", {{Parameter.Foo, "hello"},{Parameter.Bar, "bye"} }
{"DEF", {{Parameter.Baz, "hello1"},{Parameter.Foo, "bye1"} }

I would like the testList to contain

{
   TestSession("ABC", Parameter.Foo, "hello"), 
   TestSession("ABC", Parameter.Bar, "bye"), 
   TestSession("DEF", Parameter.Baz, "hello1"),
   TestSession("DEF", Parameter.Foo, "bye1")
}

The idea is that each TestSession is constructed using the Key from the inputData and the Entry<Parameter, String> from each of the entries in the list.