B. Qingshan Loves Strings
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Qingshan has a string $s$, while Daniel has a string $t$. Both strings only contain $\texttt{0}$ and $\texttt{1}$.

A string $a$ of length $k$ is good if and only if

• $a_i \ne a_{i+1}$ for all $i=1,2,\ldots,k-1$.

For example, $\texttt{1}$, $\texttt{101}$, $\texttt{0101}$ are good, while $\texttt{11}$, $\texttt{1001}$, $\texttt{001100}$ are not good.

Qingshan wants to make $s$ good. To do this, she can do the following operation any number of times (possibly, zero):

• insert $t$ to any position of $s$ (getting a new $s$).

Please tell Qingshan if it is possible to make $s$ good.

Input

The input consists of multiple test cases. The first line contains a single integer $T$ ($1\le T\le 2000$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $n$ and $m$ ($1 \le n,m \le 50$) — the length of the strings $s$ and $t$, respectively.

The second line of each test case contains a string $s$ of length $n$.

The third line of each test case contains a string $t$ of length $m$.

It is guaranteed that $s$ and $t$ only contain $\texttt{0}$ and $\texttt{1}$.

Output

For each test case, print "YES" (without quotes), if it is possible to make $s$ good, and "NO" (without quotes) otherwise.

You can print letters in any case (upper or lower).

Example
Input
51 1103 31110103 2111006 7101100101010110 2100100100010
Output
Yes
Yes
No
No
No

Note

In the first test case, $s$ is good initially, so you can get a good $s$ by doing zero operations.

In the second test case, you can do the following two operations (the inserted string $t$ is underlined):

1. $\texttt{1}\underline{\texttt{010}}\texttt{11}$
2. $\texttt{10101}\underline{\texttt{010}}\texttt{1}$

and get $s = \texttt{101010101}$, which is good.

In the third test case, there is no way to make $s$ good after any number of operations.