BrainTeaser Difficult

Problem - 2244
There are $2015$ people standing in a circle, counting $1$ and $2$ in turn continuously. Those who count $2$ will be out. For example, people who stand at initial positions of $2, 4, \dots, 2014, 1, 3, \dots$ etc will be out. The game goes on until there is only one person remaining in the circle. What is his initial position?

$(2015-1024)\times 2+1$. This problem is the same as # 4703.

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