Cyclic-Shift Substring

Problem Description

For a string, one cyclic shift is defined as moving its first character to the end to form a new string.

Given two strings $s_1$ and $s_2$, determine whether one of them is a substring of the other string after several cyclic shifts. For example, CDAA is a substring of BCDAA, which is obtained from AABCD by two shifts; whereas ABCD and ACBD cannot yield, by any number of shifts, a new string of which one is a substring.

Input Format

One line containing two strings separated by a single space. The strings contain only letters and digits, and have length at most $30$.

Output Format

If one string is a substring of the other's shifted string, output true; otherwise output false.

Sample Input

AABCD CDAA

Sample Output

true