You are given three arrays: array (a), initially consisting of (n) ones; array (b), initially consisting of (m) zeros; array (c), consisting of (m) integers from (1) to (50). We perform the following process on these arrays. The process consists of (m) stages. During the (i)-th stage, the following occurs: first, for each element of the array (a) , one of three actions is independently chosen: it is multiplied by some prime number, divided by some prime number (it cannot be divided by a number that does not divide the element evenly), or remains unchanged. You don't have to choose the same action or prime number for each element of (a); then you can either skip this step or choose any (k) such that (a_k = c_i), and assign (b_i = k). An array of (m) numbers from (0) to (n) is called achievable if it can be obtained as a result of this process as the array (b). Your task is to count the number of achievable arrays. The first line contains two integers (n) and (m) ((1 \le n, m \le 10^4)). The second line contains (m) integers (c_1, c_2, \dots, c_m) ((1 \le c_i \le 50)). Print one integer — the number of achievable arrays, taken modulo (998244353).