You are given an array (a_1,a_2,\ldots,a_n) of length (n) and a positive integer (k), but some parts of the array (a) are missing. Your task is to fill the missing part so that the maximum subarray sum (^{\text{∗}}) of (a) is exactly (k), or report that no solution exists. Formally, you are given a binary string (s) and a partially filled array (a), where: If you remember the value of (a_i), (s_i = 1) to indicate that, and you are given the real value of (a_i). If you don't remember the value of (a_i), (s_i = 0) to indicate that, and you are given (a_i = 0). All the values that you remember satisfy (|a_i| \le 10^6). However, you may use values up to (10^{18}) to fill in the values that you do not remember. It can be proven that if a solution exists, a solution also exists satisfying (|a_i| \le 10^{18}). (^{\text{∗}})The maximum subarray sum of an array (a) of length (n), i.e. (a_1, a_2, \ldots a_n) is defined as (\max_{1 \le i \le j \le n} S(i, j)) where (S(i, j) = a_i + a_{i + 1} + \ldots + a_j). 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 numbers (n,k) ((1 \le n \le 2 \cdot 10^5,1 \le k \le 10^{12})). The second line of each test case contains a binary ((01)) string (s) of length (n). The third line of each test case contains (n) numbers (a_1,a_2,\ldots,a_n) ((|a_i| \le 10^6)). If (s_i = 0), then it's guaranteed that (a_i = 0). It is guaranteed that the sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, first output (Yes) if a solution exists or (No) if no solution exists. You may print each character in either case, for example (YES) and (yEs) wil