I assume you are not using the bona fide resident test, but rather the physical presence test.
(See 2555 instructions, https://www.irs.gov/pub/irs-pdf/i2555.pdf , page 3.)
To qualify under the physical presence test you need to have been in the foreign country for 330 days during any 12 months. Those 12 months must include some time in 2017. E.g. they can either begin or end (or both) in 2017. They do NOT all need be in 2017. E.g. 1/2/2016 to 1/1/2017 would qualify.
So when TT asks you for the dates it is fine to put a 2016 date for the beginning of the period as long as the ending date is in 2017.
You still have to meet the 330 days. See the instructions for what counts.
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