Problem Statement

You are given integer sequences $A=(A_1,A_2,\dots,A_N)$ and $B=(B_1,B_2,\dots,B_M)$ of length $2$ or more, consisting of $0$s and $1$s. You can perform the following operation on $A$ any number of times:

• Choose an integer $i$ satisfying $1 \leq i \leq |A|-1$.
• Insert $1-A_i$ and $1-A_{i+1}$ in this order between $A_i$ and $A_{i+1}$.

Determine whether it is possible to make $A$ equal to $B$.

Solve $T$ test cases per input.

Constraints

• $1 \leq T \leq 10^5$
• $2 \leq N \leq M \leq 2 \times 10^5$
• $A_i, B_i \in \{0,1\}$
• The sum of $N+M$ over all test cases is at most $4 \times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each test case $\mathrm{case}_t$ is given in the following format:

N M
A_1 A_2 \dots A_N
B_1 B_2 \dots B_M

Output

Output the answers over a total of $T$ lines. The $t$-th line should contain Yes if it is possible to make $A$ equal to $B$ for the $t$-th test case, and No otherwise.