V-Sort

You are given two sequences $A=[A_1,A_2,\cdots,A_N]$ and $B=[B_1,B_2,\cdots,B_N]$ of length $N$, and two integers $X,Y$. Each element is an integer between $1$ and $N$, inclusive. Values may repeat.

You may perform the following operations any number of times, in any order, including performing no operations.

• Choose an integer $i$ with $1 \leq i \leq N-X$ and swap $A_{i+X}$ with .

Determine whether it is possible to obtain $A_i=B_i=i$ for every $i$ ($1$).

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, print YES if the target arrangement can be obtained, or NO otherwise, on a separate line.

• $1 \leq T \leq 100\,000$.
• $1 \leq N \leq 500\,000$.
• $0\le X$.