KöMaL 2019 K637

Let us consider the integer $12345678901234567890\ldots 1234567890$ consisting of 2020 digits. First we remove the digits at every odd position. Then, from the remaining 1010 digits, we remove the digits at every even position. Then, repeating in the same way, from the remaining 505 digits, we remove the digits at every odd position. This alternating process is continued until a single digit remains. Determine this digit.