Fedor works in the department of permutation transforming. Today Fedor should solve the following problem: he needs to transform the permutation $$$[p_1, p_2, \ldots, p_n]$$$ of integers $$$1, 2, \ldots, n$$$ to the permutation $$$[q_1, q_2, \ldots, q_n]$$$ using at most $$$n^3$$$ $$$k$$$-transfer operations.
Consider an array of length $$$n$$$. The $$$k$$$-transfer operation with the parameters $$$(a, b)$$$ is defined as follows: a segment of $$$k$$$ consecutive elements starting with an element at index $$$a$$$ is cut away from the array and inserted back starting with the index $$$b$$$.
More formally: consider an array $$$[t_1, t_2, \ldots, t_n]$$$ and two integers $$$a$$$ and $$$b$$$ ($$$1 \le a, b \le n - k + 1$$$). Let's create the temporary array $$$[r_1, r_2, \ldots, r_{n - k}]$$$, consisting of the numbers $$$[t_1, t_2, \ldots, t_{a - 1}, t_{a + k}, t_{a + k + 1}, \ldots, t_n]$$$. Then the result of the $$$k$$$-transfer with parameters $$$(a, b)$$$ for an array $$$t$$$ is an array, consisting of the numbers $$$[r_1, r_2, \ldots, r_{b - 1}, t_a, t_{a + 1}, \ldots, t_{a + k - 1}, r_b, r_{b + 1}, \ldots, r_{n - k}]$$$.
Fedor doesn't know how to solve the task, so he asks you to help him!
You are to solve the problem for $$$t$$$ test cases.
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases.
Each test case consists of three lines. The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n \le 100$$$).
The second line contains $$$n$$$ different integers $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$) — the permutation $$$p$$$.
The third line contains $$$n$$$ different integers $$$q_1, q_2, \ldots, q_n$$$ ($$$1 \le q_i \le n$$$) — the permutation $$$q$$$.
It's guaranteed that the sum of $$$n$$$ over all test cases doesn't exceed $$$100$$$.
Print the answer for each test case. Output your answer for a single test case in the following format.
If it's impossible to obtain a permutation $$$q_1, q_2, \ldots, q_n$$$ from a permutation $$$p_1, p_2, \ldots, p_n$$$ using $$$k$$$-transfers, print a single line consisting of the word "NO".
Otherwise, print "YES" at the first line.
The second line must contain a single integer $$$m$$$ — the number of $$$k$$$-transfers performed to obtain the permutation $$$q$$$ from the permutation $$$p$$$ ($$$0 \le m \le n^3$$$). Note that you don't need to minimize $$$m$$$. It's guaranteed that if the permutation $$$q$$$ can be obtained from the permutation $$$p$$$ using $$$k$$$-transfers, then there is a solution that requires at most $$$n^3$$$ operations.
Each of the following $$$m$$$ lines should contain two integers — parameters $$$a$$$ and $$$b$$$ for the corresponding $$$k$$$-transfer.
3 2 1 2 1 2 1 4 2 1 2 3 4 1 2 4 3 3 2 2 1 3 1 3 2
YES 0 NO YES 2 1 2 1 2
In the third test case there is another way to obtain a permutation $$$q$$$ from a permutation $$$p$$$ — a single $$$k$$$-transfer with the parameters $$$a = 2$$$, $$$b = 1$$$.
