Captive Friends

2020 men are held captive by a pirate lord, including two friends Jack and Tony.

The pirate decides to set 1010 of them free. The 2020 men are randomly divided into 1010 pairs. Each pair of men then flip a fair coin to decide who goes free.

The probability that both Jack and Tony are set free is AB\frac{A}{B} where AA and BB are co-prime positive integers. Find the value of A+B.A+B.

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