You are given an array (a) of size (n) ((1 \leq a_i \leq m)). Consider all (m!) permutations of the array (1, 2, \ldots, m). For any permutation (p), define the array (b_p) as the array formed by concatenating the array (a) and the permutation (p). More formally, (b_p = a_1, a_2, \ldots, a_n, p_1, p_2, \ldots, p_m). Let (f(i)) denote the number of permutations (p) such that the array (b_p) contains exactly (i) palindromic(^{\text{∗}}) subarrays of even length . Your task is to compute () \sum_{i=0}^{10^{100}} f(i)^{i+1}.() Since the answer may be large, it should be computed modulo (998\,244\,353). (^{\text{∗}})An array (c_1, c_2, \ldots, c_k) is said to be palindromic if (c_i = c_{k+1-i}) for all (1 \le i \le k). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^5)). The description of the test cases follows. The first line of each testcase contains two integers (n) and (m) ((1 \le m \le n \le 10^6)). The second line of each testcase contains (n) integers (a_1, a_2, \ldots, a_n) ((1 \le a_i \le m)) — the elements of the array. It is guaranteed that the sum of (n) over all test cases does not exceed (10^6). For each testcase, print a single integer on a new line — (\sum_{i=0}^{10^{100}} f(i)^{i+1}) modulo (998\,244\,353). In the first test case, (n=4), (m=3), and (a=3,1,2,1). Let's list all permutations and calculate the number of palindromic subarrays of even length: (p_1 = 1, 2, 3), (b_{p_1} = 3, 1, 2, 1, 1, 2, 3), and the number of palindromic subarrays of even length is (2). (p_2 = 1, 3, 2), (b_{p_2} = 3, 1, 2, 1, 1, 3, 2), and the number of palindromic subarrays of even length is (1). (p_3 = 2, 1, 3), (b_{p_3} = 3, 1, 2, 1, 2, 1, 3), and the number of palindromic subarrays of even length is $$$0