CF1812D Trivial Conjecture

$ $$$f(n) = \left\{ \begin{array}{ll} \frac{n}{2} & n \equiv 0 \pmod{2}\\ 3n+1 & n \equiv 1 \pmod{2}\\ \end{array} \right. $ $

Find an integer $ n $ so that none of the first $ k $ terms of the sequence $ n, f(n), f(f(n)), f(f(f(n))), \\dots $ are equal to $ 1$$$.

The only line contains an integer $ k $ ( $ 1 \leq k \leq \min(\textbf{[REDACTED]}, 10^{18}) $ ).

Output a single integer $ n $ such that none of the first $ k $ terms of the sequence $ n, f(n), f(f(n)), f(f(f(n))), \dots $ are equal to $ 1 $ . Integer $ n $ should have at most $ 10^3 $ digits.

In the first test, the sequence created with $ n = 5 $ looks like $ 5, 16, 8, 4, 2, 1, 4, \dots $ , and none of the first $ k=1 $ terms are equal to $ 1 $ . In the second test, the sequence created with $ n = 6 $ looks like $ 6, 3, 10, 5, 16, 8, 4, \dots $ , and none of the first $ k=5 $ terms are equal to $ 1 $ .