For a binary string(^{\text{∗}}) (v), the score of (v) is defined as the maximum value of ()F\big(v, 1, i\big) \cdot F\big(v, i+1, |v|\big)() over all (i) ((0 \leq i \leq |v|)). Here, (F\big(v, l, r\big) = r - l + 1 - 2 \cdot \operatorname{zero}(v, l, r)), where (\operatorname{zero}(v, l, r)) denotes the number of (\mathtt{0})s in (v_lv_{l+1} \ldots v_r). If (l > r), then (F\big(v, l, r\big) = 0). You are given a binary string (s) of length (n) and a positive integer (q). You will be asked (q) queries. In each query, you are given an integer (i) ((1 \leq i \leq n)). You must flip (s_i) from (\mathtt{0}) to (\mathtt{1}) (or from (\mathtt{1}) to (\mathtt{0})). Find the sum of the scores over all non-empty subsequences(^{\text{†}}) of (s) after each modification query. Since the result may be large, output the answer modulo (998\,244\,353). Note that the modifications are persistent. (^{\text{∗}})A binary string is a string that consists only of the characters (\mathtt{0}) and (\mathtt{1}). (^{\text{†}})A binary string (x) is a subsequence of a binary string (y) if (x) can be obtained from (y) by deleting several (possibly zero or all) characters. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains two integers (n) and (q) ((1 \leq n \leq 2 \cdot 10^5), (1 \leq q \leq 2 \cdot 10^5)) — the length of the string (s) and the number of modification queries, respectively. The second line contains the binary string (s) of length (n), consisting of characters (\mathtt{0}) and (\mathtt{1}). The following (q) lines each contain an integer (i) ((1 \leq i \leq n)), indicating that (s_i) is flipped from (\mathtt{0}) to $$$\mat