P3612 [USACO17JAN] Secret Cow Code S

The cows are experimenting with secret codes, and have devised a method for creating an infinite-length string to be used as part of one of their codes. Given a string $s$, let $F(s)$ be $s$ followed by $s$ "rotated" one character to the right (in a right rotation, the last character of $s$ rotates around and becomes the new first character). Given an initial string $s$, the cows build their infinite-length code string by repeatedly applying $F$; each step therefore doubles the length of the current string. Given the initial string and an index $N$, please help the cows compute the character at the $N$th position within the infinite code string.

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In this example, the initial string COW expands as follows: COW -> COWWCO -> COWWCOOCOWWC 12345678