Little R is a magician who likes non-decreasing arrays. She has an array of length $$$n$$$, initially as $$$a_1, \ldots, a_n$$$, in which each element is an integer between $$$[1, m]$$$. She wants it to be non-decreasing, i.e., $$$a_1 \leq a_2 \leq \ldots \leq a_n$$$.

To do this, she can perform several magic tricks. Little R has a fixed array $$$b_1\ldots b_m$$$ of length $$$m$$$. Formally, let's define a trick as a procedure that does the following things in order:

Choose a set $$$S \subseteq \{1, 2, \ldots, n\}$$$.
For each $$$u \in S$$$, assign $$$a_u$$$ with $$$b_{a_u}$$$.

Little R wonders how many tricks are needed at least to make the initial array non-decreasing. If it is not possible with any amount of tricks, print $$$-1$$$ instead.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\le t\le 10^4$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1\leq n \leq 10^6$$$, $$$1 \leq m \leq 10^6$$$) — the length of the initial array and the range of the elements in the array.

The second line of each test case contains $$$n$$$ integers $$$a_1, \ldots, a_n$$$ ($$$1 \leq a_i \leq m$$$) — the initial array.

The third line of each test case contains $$$m$$$ integers $$$b_1, \ldots, b_m$$$ ($$$1 \leq b_i \leq m$$$) — the fixed magic array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^6$$$ and the sum of $$$m$$$ over all test cases does not exceed $$$10^6$$$.

Output

For each test case, output a single integer: the minimum number of tricks needed, or $$$-1$$$ if it is impossible to make $$$a_1, \ldots, a_n$$$ non-decreasing.

Note

In the first case, the initial array $$$a_1, \ldots, a_n$$$ is $$$[1, 6, 3, 7, 1]$$$. You can choose $$$S$$$ as follows:

first trick: $$$S = [2, 4, 5]$$$, $$$a = [1, 1, 3, 5, 2]$$$;
second trick: $$$S = [5]$$$, $$$a = [1, 1, 3, 5, 3]$$$;
third trick: $$$S = [5]$$$, $$$a = [1, 1, 3, 5, 5]$$$.

So it is possible to make $$$a_1, \ldots, a_n$$$ non-decreasing using $$$3$$$ tricks. It can be shown that this is the minimum possible amount of tricks.

In the second case, it is impossible to make $$$a_1, \ldots, a_n$$$ non-decreasing.

Long Way to be Non-decreasing

Examples