Lexicographically smallest ternary

All numbers between $A$ and $B$ are written in base-three numeral system, without leading zeros. Each number is given on a separate line. Then, the resulting lines are sorted lexicographically. Which number will be first?

The numbers $A$ and $B$ are given in decimal, and the answer should also be provided in decimal.

For example, if A = 2 and B = 12:

In this case, the answer will be $3$ (since in base three it is written as $10$).