USACO

USACO 2017 January Contest, Silver

Problem 3. Secret Cow Code

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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.

INPUT FORMAT (file cowcode.in):

The input consists of a single line containing a string followed by

$N$ . The string consists of at most 30 uppercase characters, and

$N \leq 10^{18}$ .

Note that $N$ may be too large to fit into a standard 32-bit integer, so you may want to use a 64-bit integer type (e.g., a "long long" in C/C++).

OUTPUT FORMAT (file cowcode.out):

Please output the

$N$ th character of the infinite code built from the initial string. The first character is

$N=1$ .

SAMPLE INPUT:

COW 8

SAMPLE OUTPUT:

In this example, the initial string COW expands as follows:

COW -> COWWCO -> COWWCOOCOWWC
                 12345678

Problem credits: Brian Dean

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