Let's call an increase of the fraction (\frac{x}{y}) one of the following operations: either increase its numerator (x) by (1); or, if the denominator (y \gt 1), decrease its denominator (y) by (1). Note that the fraction is not reduced after the increase. For example, if you have a fraction (\frac{3}{7}) and you decrease its denominator by (1), you get (\frac{3}{6}), not (\frac{1}{2}). Suppose you are given an integer array (b_1, b_2, \dots, b_m) and an integer (k). You apply the following algorithm: Construct the array (\frac{1}{b_1}, \frac{1}{b_2}, \dots, \frac{1}{b_m}). Choose any of the fractions and increase it. Repeat the previous step (k) times (the same fraction can be chosen multiple times). Calculate the sum of the resulting fractions. We will denote (\mathrm{MSF}(b, k)) as the maximum sum of fractions that can be obtained from the array (b) by applying the increase operation exactly (k) times. Let (al \dots r) be the subarray (a_l, a_{l + 1}, \dots a_r) of the array (a). You are given two arrays of integers (a_1, a_2, \dots, a_n) and (k_1, k_2, \dots, k_m). For each (k_i), calculate ()\left( \sum\limits_{l = 1}^{n}{\sum\limits_{r = l}^{n}\mathrm{MSF}(al \dots r, k_i)} \right) \bmod 998\,244\,353.() In other words, for each (k_i), calculate the sum of (\mathrm{MSF}) over all subarrays of the array (a) and output the answer modulo. The first line contains two integers (n) and (m) ((1 \le n, m \le 5 \cdot 10^5)) — the sizes of the arrays (a) and (k). The second line contains (n) integers (a_1, a_2, \dots, a_n) ((1 \le a_i \le 10^8)) — the array (a). The third line contains (m) integers (k_1, k_2, \dots, k_m) ((0 \le k_1 \le k_2 \le \dots \le k_m \le 10^8)) — the array (k) in non-decreasing order. For each (k_i), output a single integer — the sum of (\mathrm{MSF}) over all su