CF2231D Maximum Prefix Sums

521 sounds the same as "I love you" in Chinese. On this special day, Little S wants to give Little A some well-prepared sequences to recall their friendship sealed for years. Little S has prepared an array $ a_1, a_2, \ldots, a_n $ . Let's define its prefix sums array $ b_1, b_2, \ldots, b_n $ , where $ b_i = a_1 + a_2 + \ldots + a_i $ . Also define the prefix maximum array of $ b $ : $ c_1, c_2, \ldots, c_n $ , where $ c_i = \max(b_1, b_2, \ldots, b_i) $ . Now array $ a $ has been partially lost, but luckily Little S still keeps the array $ c $ . Your task is to restore the array $ a $ and send it to Little A, or report that no such array exists — in this case, the kind and cute Little A won't get mad either. Formally, you are given a binary string $ s $ , a partially filled array $ a $ , and an array $ c $ , where: - If you remember the value of $ a_i $ , then $ s_i = 1 $ , and you are given the true value of $ a_i $ . - If you do not remember the value of $ a_i $ , then $ s_i = 0 $ , and you are given $ a_i = 0 $ .

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 an integer $ n $ ( $ 1 \le n \le 2 \cdot 10^5 $ ). The second line of each test case contains a binary string $ s $ ( $ s_i \in \{\texttt{0}, \texttt{1}\} $ ) of length $ n $ . The third line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ |a_i| \le 10^6 $ ). If $ s_i = \texttt{0} $ , then it is guaranteed that $ a_i = 0 $ . The fourth line of each test case contains $ n $ integers $ c_1, c_2, \ldots, c_n $ ( $ |c_i| \le 2 \cdot 10^{11} $ ). It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, print "Yes" in the first line if the array $ a $ exists, otherwise print "No". You may print the answer in any case. For example, "YeS", "YES", "NO", "nO" will also be accepted. If there is at least one solution, print $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ |a_i| \leq 10^{18} $ ) in the second line. If there are multiple suitable arrays, you may print any of them.

In the first test case, we have: - $ a = [1, 2, -1, 0] $ . - $ b = [1, 3, 2, 2] $ . - $ c = [1, 3, 3, 3] $ . In the third test case, the correct array $ a $ should be equal to $ [1] $ , so no solution exists.