Qingshan has a string $s$, while Daniel has a string $t$. Both strings only contain 0 and 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, 1, 101, 0101 are good, while 11, 1001, 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 0 and 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).

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

Samples

5
1 1
1
0
3 3
111
010
3 2
111
00
6 7
101100
1010101
10 2
1001001000
10

Yes
Yes
No
No
No