You are given a sequence (a) of length (n) and a positive integer (m). Each element of (a) is an integer in the range (0, m). A sequence (a) is considered good if and only if the following two conditions hold: (a_1<a_2<a_3<\ldots<a_n), and (\frac{1}{\operatorname{lcm}(a_1,a_2)}+\frac{1}{\operatorname{lcm}(a_2,a_3)}+\ldots+\frac{1}{\operatorname{lcm}(a_{n-1},a_n)}+\color{red}{\frac{1}{\operatorname{lcm}(a_n,a_1)}}\ge1).(^{\text{∗}}) You need to replace all zeros in (a) with integers from the range (1, m). Calculate the number of different ways to replace the zeros such that the resulting sequence (a) is good . Print the answer modulo (998\,244\,353). (^{\text{∗}})The Least common multiple ((\operatorname{lcm})) of two positive integers is the smallest positive integer that is a multiple of both. For example, (\operatorname{lcm}(2,3)=6, \operatorname{lcm}(4,6)=12). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 1000)). The description of the test cases follows. The first line of each test case contains two integers (n) and (m) ((2 \le n\le m \le 3000)). The second line of each test case contains (n) integers (a_1, a_2, \ldots, a_n) ((0 \le a_i \le m)). It is guaranteed that the sum of (m) over all test cases does not exceed (3000). For each test case, output a single integer — the number of ways to complete the sequence so that it becomes good, modulo (998\,244\,353). In the first test case, there are (2) ways to replace the zeros such that the sequence becomes good: (1, 2, 3, 6): The sum is (\frac{1}{\operatorname{lcm}(1, 2)} + \frac{1}{\operatorname{lcm}(2, 3)} + \frac{1}{\operatorname{lcm}(3, 6)} + \frac{1}{\operatorname{lcm}(6, 1)} = \frac{1}{2} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = 1). (1, 2, 4, 6): The sum is $$$\frac{1}{\operatorname{lcm}(1, 2)} + \frac{1}{