Reverse String
Contest: Harbour.Space Scholarship Contest 2021-2022 (open for everyone, rated, Div. 1 + Div. 2)
Difficulty rating: 1300
Tags: brute force, dp, hashing, implementation, strings

You have a string $$$s$$$ and a chip, which you can place onto any character of this string.

After placing the chip, you move it to the right several (maybe zero) times, i. e. you perform the following operation several times: if the current position of the chip is $$$i$$$, you move it to the position $$$i + 1$$$. Of course, moving the chip to the right is impossible if it is already in the last position.

After moving the chip to the right, you move it to the left several (maybe zero) times, i. e. you perform the following operation several times: if the current position of the chip is $$$i$$$, you move it to the position $$$i - 1$$$. Of course, moving the chip to the left is impossible if it is already in the first position.

When you place a chip or move it, you write down the character where the chip ends up after your action. For example, if $$$s$$$ is abcdef, you place the chip onto the $$$3$$$-rd character, move it to the right $$$2$$$ times and then move it to the left $$$3$$$ times, you write down the string cdedcb.

You are given two strings $$$s$$$ and $$$t$$$. Your task is to determine whether it's possible to perform the described operations with $$$s$$$ so that you write down the string $$$t$$$ as a result.

Input format:
The first line contains one integer $$$q$$$ ($$$1 \le q \le 500$$$) — the number of test cases.

Each test case consists of two lines. The first line contains the string $$$s$$$ ($$$1 \le |s| \le 500$$$), the second line contains the string $$$t$$$ ($$$1 \le |t| \le 2 \cdot |s| - 1$$$). Both strings consist of lowercase English characters.

It is guaranteed that the sum of $$$|s|$$$ over all test cases does not exceed $$$500$$$.

Output format:
For each test case, print "YES" if you can obtain the string $$$t$$$ by performing the process mentioned in the statement with the string $$$s$$$, or "NO" if you cannot.

You may print each letter in any case (YES, yes, Yes will all be recognized as positive answer, NO, no and nO will all be recognized as negative answer).

Constraints:
Time limit: 3.0 s
Memory limit: 256.0 MB

Note:
Consider the examples.

The first test case is described in the statement.

In the second test case, you can place the chip on the $$$1$$$-st position, move it twice to the right, and then move it twice to the left.

In the fourth test case, you can place the chip on the $$$2$$$-nd position, and then don't move it at all.

In the fifth test case, you can place the chip on the $$$1$$$-st position, move it $$$5$$$ times to the right, and then finish the process.

Example input:
6
abcdef
cdedcb
aaa
aaaaa
aab
baaa
ab
b
abcdef
abcdef
ba
baa

Example output:
YES
YES
NO
YES
YES
NO

Editorial:
Let's iterate over starting positions, the number of times we go to the right and the number of times we go to the left. After that we can check that resulting string is equal to the needed one. This solution works in $$$O(n^4)$$$, since there are $$$O(n^3)$$$ possible combinations of starting position, number of moves to the right and left and each check can take up to $$$O(n)$$$ time. To optimize this solution we can notice that if we know number of moves to the right then we can recover number of moves to the left(because we know the length of needed string). So, we have $$$O(n^2)$$$ possible combinations, that's why this solution works in $$$O(n^3)$$$, which is enough to pass tests.
Can you solve this problem in $$$O(n^2)$$$ time? Maybe even faster?