Description

For a string, a cyclic shift operation is defined as: moving the first character of the string to the end to form a new string.
Given two strings $s_1$ and $s_2$, determine if one string is a substring of the other string after some number of cyclic shifts. For example, $CDAA$ is a substring of $BCDAA$, which is obtained by shifting $AABCD$ twice, while $ABCD$ and $ACBD$ cannot be obtained through multiple shifts to make one string a substring of the other.

Input Format

One line containing two strings separated by a single space. The strings contain only letters and digits, with length not exceeding $30$.

Output Format

If one string is a substring of the other string after some number of cyclic shifts, output "$true$"; otherwise, output "$false$".

Sample

AABCD CDAA

true