Skibidus thinks he's Him! He proved it by solving this difficult task. Can you also prove yourself? Given a binary string(^{\text{∗}}) (t), (f(t)) is defined as the minimum number of contiguous substrings, each consisting of identical characters, into which (t) can be partitioned. For example, (f(00110001) = 4) because (t) can be partitioned as (00110001) where each bracketed segment consists of identical characters. Skibidus gives you a binary string (s) and (q) queries. In each query, a single character of the string is flipped (i.e. (0) changes to (1) and (1) changes to (0)); changes are saved after the query is processed. After each query, output the sum over all (f(b)) where (b) is a non-empty subsequence(^{\text{†}}) of (s), modulo (998\,244\,353). (^{\text{∗}})A binary string consists of only characters (0) and (1). (^{\text{†}})A subsequence of a string is a string which can be obtained by removing several (possibly zero) characters from the original string. The first line contains an integer (t) ((1 \leq t \leq 10^4)) — the number of test cases. The first line of each test case contains a binary string (s) ((1 \leq |s| \leq 2 \cdot 10^5)). The following line of each test case contains an integer (q) ((1 \leq q \leq 2 \cdot 10^5)) — the number of queries. The following line contains (q) integers (v_1, v_2, \ldots, v_q) ((1 \leq v_i \leq |s|)), denoting (s_{v_i}) is flipped for the (i)'th query. It is guaranteed that the sum of (|s|) and the sum of (q) over all test cases does not exceed (2 \cdot 10^5). For each test case, output (q) integers on a single line — the answer after each query modulo (998\,244\,353). In the first test case, (s) becomes (001) after the first query. Let's calculate the answer fo