Cyclic Rotations

You are given two binary strings $A$ and $B$. Count the left cyclic rotations of $B$ whose bitwise XOR with $A$ is zero in every position.

For a string $P = P_0 P_1 \dots P_{N-1}$ of length $N$, rotating $P$ left $k$ times produces the string whose character at position $i$ is $P_{(i+k) \bmod N}$. The shift amount $k$ is an integer with $0 \le k < N$, and two shifts with different $k$ count separately even when they produce the same string.

The first line contains $A$ and the second line contains $B$. Both strings consist of the characters 0 and 1 only and have the same length, which is between 1 and $10^5$.

Print the number of cyclic rotations of $B$ whose XOR with $A$ is zero in every position.