AT_abc427_g [ABC427G] Takahashi's Expectation 2

Takahashi will receive some presents from now on. He has an integer parameter called mood, and the mood changes each time he receives a present. Each present has an integer parameter called value $ P $ , and Takahashi's mood changes according to this parameter as follows: - If the value $ P $ of the received present is greater than or equal to the mood value, he is delighted with the present, and the mood increases by $ A $ . - If the value $ P $ of the received present is less than the mood value, he is disappointed with the present, and the mood decreases by $ B $ . Initially, there are $ N $ presents that Takahashi is scheduled to receive, and the value of the $ i $ -th present he will receive $ (1\le i\le N) $ is $ P _ i $ . You are given $ Q $ queries consisting of two types: addition queries and question queries. Process all of them in order, and answer all question queries. The $ i $ -th query is represented by two integers $ T _ i,X _ i $ , and it is an addition query if $ T _ i=1 $ , and a question query if $ T _ i=2 $ . In an addition query, add a new present with value $ X _ i $ to the end of the presents to be received. In a question query, answer the following question: > Find Takahashi's mood after receiving all the presents he is scheduled to receive when his mood is initially $ X _ i $ .

The input is given from Standard Input in the following format: > $ N $ $ A $ $ B $ $ P _ 1 $ $ P _ 2 $ $ \ldots $ $ P _ N $ $ Q $ $ T _ 1 $ $ X _ 1 $ $ T _ 2 $ $ X _ 2 $ $ \vdots $ $ T _ Q $ $ X _ Q $

Let $ q $ be the number of question queries, and print $ q $ lines. The $ i $ -th line $ (1\le i\le q) $ should contain the answer to the $ i $ -th question query.

### Sample Explanation 1 Initially, the values of the presents Takahashi is scheduled to receive are $ 59,-26,53,58 $ , in the order he will receive them. The five queries are as follows: - When his mood is initially $ 9 $ , his mood changes as $ 9\rightarrow40\rightarrow-1\rightarrow30\rightarrow61 $ each time he receives a present, so print the final mood $ 61 $ . - A present with value $ 79 $ is added to the presents he is scheduled to receive, and the values of the presents he is scheduled to receive become $ 59,-26,53,58,79 $ . - When his mood is initially $ 32 $ , his mood changes as $ 32\rightarrow63\rightarrow22\rightarrow53\rightarrow84\rightarrow43 $ each time he receives a present, so print the final mood $ 43 $ . - A present with value $ 38 $ is added to the presents he is scheduled to receive, and the values of the presents he is scheduled to receive become $ 59,-26,53,58,79,38 $ . - When his mood is initially $ 462 $ , his mood changes as $ 462\rightarrow421\rightarrow380\rightarrow339\rightarrow298\rightarrow257\rightarrow216 $ each time he receives a present, so print the final mood $ 216 $ . ### Sample Explanation 2 Note that the absolute value of the input and the values to be output may be $ 2 ^ {32} $ or greater. ### Constraints - $ 1\le N\le2\times10 ^ 5 $ - $ 1\le A\le10 ^ 9 $ - $ 1\le B\le10 ^ 9 $ - $ -10 ^ 9\le P _ i\le10 ^ 9\ (1\le i\le N) $ - $ 1\le Q\le2\times10 ^ 5 $ - $ T _ i=1 $ or $ T _ i=2\ (1\le i\le Q) $ - There exists an integer $ i\ (1\le i\le Q) $ such that $ T _ i=2 $ . - If $ T _ i=1 $ , then $ -10 ^ 9\le X _ i\le10 ^ 9 $ . $ (1\le i\le Q) $ - If $ T _ i=2 $ , then $ -10 ^ {12}\le X _ i\le10 ^ {12} $ . $ (1\le i\le Q) $ - All input values are integers.