You are given three positive integers (x), (y), and (k). You are also given a binary string(^{\text{∗}}) (a) ((|a| = x + y)). Count the number of binary strings (b), modulo (998\,244\,353), such that: there are exactly (x) (\mathtt{0}) in (b). there are exactly (y) (\mathtt{1}) in (b). there exists an integer (i) ((1 \leq i \leq x + y - 1)) such that (\min \left( f(b_1 b_2 \ldots b_i), f(b_{i+1} b_{i+2} \ldots b_{x+y})\right) \geq k), where (f(s)) gives the length of the longest non-decreasing subsequence(^{\text{†}}) in (s). (b) is lexicographically larger(^{\text{‡}}) than (a). (^{\text{∗}})A binary string is a string that only consists of characters (\mathtt{0}) and (\mathtt{1}). (^{\text{†}})A sequence (a) is a subsequence of a sequence (b) if (a) can be obtained from (b) by the deletion of several (possibly, zero or all) elements. For example, subsequences of (\mathtt{1011101}) are (\mathtt{0}), (\mathtt{1}), (\mathtt{11111}), (\mathtt{0111}), but not (\mathtt{000}) nor (\mathtt{11100}). (^{\text{‡}})A string (p) is lexicographically larger than another string (q) if and only if one of the following holds: (q) is a prefix of (p), but (p \ne q); or in the first position where (p) and (q) differ, the string (p) has a larger element than the corresponding element in (q). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 5000)). The description of the test cases follows. The first line of each test case contains three integers (x), (y), and (k) ((1 \le x, y \le 5000), (1 \leq k < x + y)). The second line of each test case contains a binary string (a) ((|a| = x+y)) consisting of characters (\mathtt{0}) and (\mathtt{1}). It is guaranteed that neither the sum of (x)