J. Jewels Building
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

You are playing a fantasy game where you start with a row of $$$n$$$ power crystals. The $$$i$$$-th crystal has energy level $$$a_i$$$.

You can perform the following operation any number of times:

  • choose a consecutive group of identical crystals, that is, choose $$$l$$$ and $$$r$$$ ($$$1 \leq l \leq r \leq |a|$$$) such that $$$a_l = a_{l+1} = \ldots = a_r$$$;
  • fuse them into a single crystal whose energy becomes $$$r - l + 1$$$, obtaining the new sequence $$$[a_1, \ldots, a_{l-1}, r-l+1, a_{r+1}, \ldots, a_{|a|}]$$$.

Note that you may also choose $$$l = r$$$.

You want to craft a specific configuration of crystals with energy levels $$$b_1, \ldots, b_m$$$. Determine whether it is possible.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \leq t \leq 500$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$, $$$m$$$ ($$$1 \leq m \leq n \leq 4000$$$) — the number of crystals in the initial and target configurations, respectively.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the energy levels of the initial crystals.

The third line of each test case contains $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$ ($$$1 \leq b_i \leq 10^9$$$) — the desired energy levels of the target crystals.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$4000$$$.

Output

For each test case, output $$$\texttt{YES}$$$ if you can transform the initial configuration into the target one, and $$$\texttt{NO}$$$ otherwise.

The judge is case-insensitive (for example, $$$\texttt{YES}$$$, $$$\texttt{Yes}$$$, $$$\texttt{yes}$$$, $$$\texttt{yEs}$$$ will all be recognized as positive answers).

Example
Input
3
5 1
2 4 4 2 3
2
5 2
2 4 4 2 3
4 4
1 1
2
1
Output
YES
NO
YES
Note

Explanation of sample 1. In the first test case:

  • the initial configuration is $$$[2, 4, 4, 2, 3]$$$;
  • after fusing the two crystals in the subarray $$$[l, r] = [2, 3]$$$, the configuration becomes $$$[2, 2, 2, 3]$$$;
  • after fusing crystals in the subarray $$$[l, r] = [1, 3]$$$, the configuration becomes $$$[3, 3]$$$;
  • after fusing crystals in the subarray $$$[l, r] = [1, 2]$$$, the configuration becomes $$$[2] = [b_1]$$$. So the answer is $$$\texttt{YES}$$$.

In the second test case, it is not possible to obtain $$$[4, 4]$$$ starting from $$$[2, 4, 4, 2, 3]$$$, so the answer is $$$\texttt{NO}$$$.