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 $n, k$ ($1 \le k < n \le 200\,000$): 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 $998\,244\,353$.


-----Example-----
Input
3
5 3
1 2 3 4 5
3 2 5
4 3
4 3 2 1
4 3 1
7 4
1 4 7 3 6 2 5
3 2 4 5

Output
2
0
4



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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ninput = sys.stdin.readline\nt = int(input())\nfor _ in range(t):\n    n, k = list(map(int, input().split()))\n    a = list(map(int, input().split()))\n    r = [0] * n\n    for i in range(n):\n        r[a[i] - 1] = i\n    b = list(map(int, input().split()))\n    d = [0] * n\n    for i in range(k):\n        d[b[i] - 1] = 1\n    cnt = 0\n    for i in range(k):\n        idx = r[b[i] - 1]\n        t = 0\n        if idx > 0 and d[a[idx - 1] - 1] == 0:\n            t += 1\n        if idx < n - 1 and d[a[idx + 1] - 1] == 0:\n            t += 1\n        if t == 0:\n            print(0)\n            break\n        elif t == 2:\n            cnt += 1\n        d[b[i] - 1] = 0\n    else:\n        print(pow(2, cnt, 998244353))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13685