B'There is a hidden array a_1, a_2, ldots, a_n of length n whose elements are integers between -m and m , inclusive. You are given an array b_1, b_2, ldots, b_n of length n and a string s of length n consisting of the characters texttt{P} , texttt{S} , and texttt{?} . For each i from 1 to n inclusive, we must have: Output the number of ways to replace all texttt{?} in s with either texttt{P} or texttt{S} such that there exists an array a_1, a_2, ldots, a_n with elements not exceeding m by absolute value satisfying the constraints given by the array b_1, b_2, ldots, b_n and the string s . Since the answer may be large, output it modulo 998 ,244 ,353 . The first line contains a single integer t ( 1 <= q t <= q 10^3 ) -- the number of test cases. The first line of each test case contains two integers n and m ( 2 <= q n <= q 2 cdot 10^3 , 2 <= q m <= q 10^{9} ) -- the length of the hidden array a_1, a_2, ldots, a_n and the maximum absolute value of an element a_i . The second line of each test case contains a string s of length n consisting of characters texttt{P} , texttt{S} , and texttt{?} . The third line of each test case contains n integers b_1, b_2, ldots, b_n ( |b_i| <= q m cdot n ). The sum of n over all test cases does not exceed 5 cdot 10^3 . For each test case, output a single integer -- the number of ways to replace all texttt{?} in s with either texttt{P} or texttt{S} that result in the existence of a valid array a_1, a_2, ldots, a_n , modulo 998 ,244 ,353 . In the first test case, we can see that the following array satisfies all constraints, thus the answer is 1 : In the second test case, it can be shown that no array a with all |a_i| <= q m = 10^'...