We start with a permutation $$$a_1, a_2, \ldots, a_n$$$ and with an empty array $$$b$$$. We apply the following operation $$$k$$$ times.

On the $$$i$$$-th iteration, we select an index $$$t_i$$$ ($$$1 \le t_i \le n-i+1$$$), remove $$$a_{t_i}$$$ from the array, and append one of the numbers $$$a_{t_i-1}$$$ or $$$a_{t_i+1}$$$ (if $$$t_i-1$$$ or $$$t_i+1$$$ are within the array bounds) to the right end of the array $$$b$$$. Then we move elements $$$a_{t_i+1}, \ldots, a_n$$$ to the left in order to fill in the empty space.

You are given the initial permutation $$$a_1, a_2, \ldots, a_n$$$ and the resulting array $$$b_1, b_2, \ldots, b_k$$$. All elements of an array $$$b$$$ are distinct. Calculate the number of possible sequences of indices $$$t_1, t_2, \ldots, t_k$$$ modulo $$$998\,244\,353$$$.

Input

Each test contains multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \le t \le 100\,000$$$), denoting the number of test cases, followed by a description of the test cases.

The first line of each test case contains two integers $$$n, k$$$ ($$$1 \le k \lt n \le 200\,000$$$): sizes of arrays $$$a$$$ and $$$b$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$): elements of $$$a$$$. All elements of $$$a$$$ are distinct.

The third line of each test case contains $$$k$$$ integers $$$b_1, b_2, \ldots, b_k$$$ ($$$1 \le b_i \le n$$$): elements of $$$b$$$. All elements of $$$b$$$ are distinct.

The sum of all $$$n$$$ among all test cases is guaranteed to not exceed $$$200\,000$$$.

Output

For each test case print one integer: the number of possible sequences modulo $$$998\,244\,353$$$.

Note

$$$\require{cancel}$$$

Let's denote as $$$a_1 a_2 \ldots \cancel{a_i} \underline{a_{i+1}} \ldots a_n \rightarrow a_1 a_2 \ldots a_{i-1} a_{i+1} \ldots a_{n-1}$$$ an operation over an element with index $$$i$$$: removal of element $$$a_i$$$ from array $$$a$$$ and appending element $$$a_{i+1}$$$ to array $$$b$$$.

In the first example test, the following two options can be used to produce the given array $$$b$$$:

$$$1 2 \underline{3} \cancel{4} 5 \rightarrow 1 \underline{2} \cancel{3} 5 \rightarrow 1 \cancel{2} \underline{5} \rightarrow 1 2$$$; $$$(t_1, t_2, t_3) = (4, 3, 2)$$$;
$$$1 2 \underline{3} \cancel{4} 5 \rightarrow \cancel{1} \underline{2} 3 5 \rightarrow 2 \cancel{3} \underline{5} \rightarrow 1 5$$$; $$$(t_1, t_2, t_3) = (4, 1, 2)$$$.

In the second example test, it is impossible to achieve the given array no matter the operations used. That's because, on the first application, we removed the element next to $$$4$$$, namely number $$$3$$$, which means that it couldn't be added to array $$$b$$$ on the second step.

In the third example test, there are four options to achieve the given array $$$b$$$:

$$$1 4 \cancel{7} \underline{3} 6 2 5 \rightarrow 1 4 3 \cancel{6} \underline{2} 5 \rightarrow \cancel{1} \underline{4} 3 2 5 \rightarrow 4 3 \cancel{2} \underline{5} \rightarrow 4 3 5$$$;
$$$1 4 \cancel{7} \underline{3} 6 2 5 \rightarrow 1 4 3 \cancel{6} \underline{2} 5 \rightarrow 1 \underline{4} \cancel{3} 2 5 \rightarrow 1 4 \cancel{2} \underline{5} \rightarrow 1 4 5$$$;
$$$1 4 7 \underline{3} \cancel{6} 2 5 \rightarrow 1 4 7 \cancel{3} \underline{2} 5 \rightarrow \cancel{1} \underline{4} 7 2 5 \rightarrow 4 7 \cancel{2} \underline{5} \rightarrow 4 7 5$$$;
$$$1 4 7 \underline{3} \cancel{6} 2 5 \rightarrow 1 4 7 \cancel{3} \underline{2} 5 \rightarrow 1 \underline{4} \cancel{7} 2 5 \rightarrow 1 4 \cancel{2} \underline{5} \rightarrow 1 4 5$$$;

Identify the Operations

Examples