Sacred Number

All the Smeshariki love listening to the stories of the wise old crow-artist, Kar Karych. They are particularly fond of his tales about travels to distant lands. Today, they have gathered to enjoy some delicious tea with cookies and hear his stories about mysterious faraway places. Kar Karych did not disappoint them and shared his adventures on the islands.

On a remote island in the Pacific Ocean, the Ululu-ololo tribe celebrates the festival of $1000$ gods every year. The number $1000$ holds sacred significance for the tribe, and they believe that all other numbers are subordinate to it. To demonstrate this belief, during the festival, the chief asks the high priest to take a natural number $n$ and transform it into the sacred number. Unfortunately, the high priest is not skilled in mathematics and can only perform two operations on the number: subtract $1$ or multiply it by $2$. The sun sets early on the island, so the high priest cannot perform more than $50$ operations. If he fails to achieve the sacred number, the gods will be displeased and punish the tribe. However, the tribe will likely punish the priest first, and their punishment will be severe!

Nyusha feels sorry for the high priest, thinking that not every number can be transformed into $1000$, especially with only $2$ operations available. Kar Karych wants to reassure Nyusha and prove that the high priest can always protect the tribe from the gods' wrath by achieving the sacred number. Unfortunately, Kar Karych, like the high priest, is not very adept at mathematics, so he seeks your assistance!