Problem Statement

You are given integer sequences of length $N$: $A=(A_1,A_2,\cdots,A_N)$ and $B=(B_1,B_2,\cdots,B_N)$, and an integer $K$.

You can perform the following operation zero or more times.

• Choose integers $i$ and $j$ ($1 \leq i,j \leq N$). Here, $|i-j| \leq K$ must hold. Then, change the value of $A_i$ to $A_j$.

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

There are $T$ test cases for each input.

Constraints

• $1 \leq T \leq 125000$
• $1 \leq K < N \leq 250000$
• $1 \leq A_i,B_i \leq N$
• The sum of $N$ across all test cases in each input is at most $250000$.
• All input values are integers.

Input

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

T
case_1
case_2
\vdots
case_T

Each test case is given in the following format:

N K
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_N

Output

For each test case, print Yes if it is possible to make $A$ identical to $B$, and No otherwise.