Camp Schedule
Contest: Codeforces Round 545 (Div. 1)
Difficulty rating: 1600
Tags: greedy, hashing, strings

The new camp by widely-known over the country Spring Programming Camp is going to start soon. Hence, all the team of friendly curators and teachers started composing the camp's schedule. After some continuous discussion, they came up with a schedule $$$s$$$, which can be represented as a binary string, in which the $$$i$$$-th symbol is '1' if students will write the contest in the $$$i$$$-th day and '0' if they will have a day off.

At the last moment Gleb said that the camp will be the most productive if it runs with the schedule $$$t$$$ (which can be described in the same format as schedule $$$s$$$). Since the number of days in the current may be different from number of days in schedule $$$t$$$, Gleb required that the camp's schedule must be altered so that the number of occurrences of $$$t$$$ in it as a substring is maximum possible. At the same time, the number of contest days and days off shouldn't change, only their order may change.

Could you rearrange the schedule in the best possible way?

Input format:
The first line contains string $$$s$$$ ($$$1 \leqslant |s| \leqslant 500\,000$$$), denoting the current project of the camp's schedule.

The second line contains string $$$t$$$ ($$$1 \leqslant |t| \leqslant 500\,000$$$), denoting the optimal schedule according to Gleb.

Strings $$$s$$$ and $$$t$$$ contain characters '0' and '1' only.

Output format:
In the only line print the schedule having the largest number of substrings equal to $$$t$$$. Printed schedule should consist of characters '0' and '1' only and the number of zeros should be equal to the number of zeros in $$$s$$$ and the number of ones should be equal to the number of ones in $$$s$$$.

In case there multiple optimal schedules, print any of them.

Constraints:
Time limit: 1.0 s
Memory limit: 512.0 MB

Note:
In the first example there are two occurrences, one starting from first position and one starting from fourth position.

In the second example there is only one occurrence, which starts from third position. Note, that the answer is not unique. For example, if we move the first day (which is a day off) to the last position, the number of occurrences of $$$t$$$ wouldn't change.

In the third example it's impossible to make even a single occurrence.

Example input:
101101
110

Example output:
110110

Example input:
10010110
100011

Example output:
01100011

Editorial:
If we can't make any occurrences of string $$$t$$$ in string $$$s$$$ just output any permutation of $$$s$$$.
Otherwise, we can show that there is an optimal answer $$$x$$$, such that it starts with a string $$$t$$$.
Suppose the opposite, then remove all characters of the string $$$s$$$ before the first occurrence of the string $$$t$$$ and insert them to the end. The number of occurrences clearly didn't decreased.
Obviously, we want to make the next occurrence of string $$$t$$$ in string $$$s$$$ as left as possible. If we decide to make it somewhere else, we can move out the extra characters and try to improve the answer. To achieve this, we need to find the largest suffix of the string $$$t$$$ that matches the prefix of string $$$t$$$ of the same length. It can be found by using the prefix function, z-function or hashes.