The king returns

Logic Level 3

A king has K K servants. He ordered them to stand in a circle and numbered them from 1 to K K .

He gave to number 1 a sword and ordered him to kill the one next in number and pass the sword until only one left.
(1 kills 2 and passes to 3 and so on)

how many servants the king need to make the K K numbered servant to stay last?

Note : K K can be 1 but not 0

Take N N as a positive integer.

2 N 2^{N} 2 N 2^{N} -1 3 N 3^{N} 3 N 3^{N} -1 2 N 1 2^{N-1}

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