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#4006

Secret Cow Code 2s 512MB

문제

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 Nth position within the infinite code string.

Problem credits: Brian Dean


입력

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++).


출력

Please output the Nth character of the infinite code built from the initial string. The first character is N=1.


예제 

COW 8
C

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

COW -> COWWCO -> COWWCOOCOWWC
                 12345678


출처

USACO 2017 January Silver
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