Petya and Exam

题意翻译

Petya将会参加一场考试，这场考试从时间点0开始，到T结束。考试中有n道题，分为两种，简单（需要花a时间做完）的题和困难（需要花b时间做完）的题（a <= b），即在时间点x开始做这道题，将会在x+a或x+b时间点完成。现在每道题会在时间点 ti 变成必须完成，Petya可以在0 ~ T任意一个时间点离开，若离开时有必须要完成的题目没有完成，他将会得到0分，否则会得到他完成的题目的分数。求他最大能得到的分数。

题目描述

Petya has come to the math exam and wants to solve as many problems as possible. He prepared and carefully studied the rules by which the exam passes. The exam consists of $ n $ problems that can be solved in $ T $ minutes. Thus, the exam begins at time $ 0 $ and ends at time $ T $ . Petya can leave the exam at any integer time from $ 0 $ to $ T $ , inclusive. All problems are divided into two types: - easy problems — Petya takes exactly $ a $ minutes to solve any easy problem; - hard problems — Petya takes exactly $ b $ minutes ( $ b > a $ ) to solve any hard problem. Thus, if Petya starts solving an easy problem at time $ x $ , then it will be solved at time $ x+a $ . Similarly, if at a time $ x $ Petya starts to solve a hard problem, then it will be solved at time $ x+b $ . For every problem, Petya knows if it is easy or hard. Also, for each problem is determined time $ t_i $ ( $ 0 \le t_i \le T $ ) at which it will become mandatory (required). If Petya leaves the exam at time $ s $ and there is such a problem $ i $ that $ t_i \le s $ and he didn't solve it, then he will receive $ 0 $ points for the whole exam. Otherwise (i.e if he has solved all such problems for which $ t_i \le s $ ) he will receive a number of points equal to the number of solved problems. Note that leaving at time $ s $ Petya can have both "mandatory" and "non-mandatory" problems solved. For example, if $ n=2 $ , $ T=5 $ , $ a=2 $ , $ b=3 $ , the first problem is hard and $ t_1=3 $ and the second problem is easy and $ t_2=2 $ . Then: - if he leaves at time $ s=0 $ , then he will receive $ 0 $ points since he will not have time to solve any problems; - if he leaves at time $ s=1 $ , he will receive $ 0 $ points since he will not have time to solve any problems; - if he leaves at time $ s=2 $ , then he can get a $ 1 $ point by solving the problem with the number $ 2 $ (it must be solved in the range from $ 0 $ to $ 2 $ ); - if he leaves at time $ s=3 $ , then he will receive $ 0 $ points since at this moment both problems will be mandatory, but he will not be able to solve both of them; - if he leaves at time $ s=4 $ , then he will receive $ 0 $ points since at this moment both problems will be mandatory, but he will not be able to solve both of them; - if he leaves at time $ s=5 $ , then he can get $ 2 $ points by solving all problems. Thus, the answer to this test is $ 2 $ . Help Petya to determine the maximal number of points that he can receive, before leaving the exam.

输入输出格式

输入格式

The first line contains the integer $ m $ ( $ 1 \le m \le 10^4 $ ) — the number of test cases in the test. The next lines contain a description of $ m $ test cases. The first line of each test case contains four integers $ n, T, a, b $ ( $ 2 \le n \le 2\cdot10^5 $ , $ 1 \le T \le 10^9 $ , $ 1 \le a < b \le 10^9 $ ) — the number of problems, minutes given for the exam and the time to solve an easy and hard problem, respectively. The second line of each test case contains $ n $ numbers $ 0 $ or $ 1 $ , separated by single space: the $ i $ -th number means the type of the $ i $ -th problem. A value of $ 0 $ means that the problem is easy, and a value of $ 1 $ that the problem is hard. The third line of each test case contains $ n $ integers $ t_i $ ( $ 0 \le t_i \le T $ ), where the $ i $ -th number means the time at which the $ i $ -th problem will become mandatory. It is guaranteed that the sum of $ n $ for all test cases does not exceed $ 2\cdot10^5 $ .

输出格式

Print the answers to $ m $ test cases. For each set, print a single integer — maximal number of points that he can receive, before leaving the exam.

输入输出样例

输入样例 #1

10
3 5 1 3
0 0 1
2 1 4
2 5 2 3
1 0
3 2
1 20 2 4
0
16
6 20 2 5
1 1 0 1 0 0
0 8 2 9 11 6
4 16 3 6
1 0 1 1
8 3 5 6
6 20 3 6
0 1 0 0 1 0
20 11 3 20 16 17
7 17 1 6
1 1 0 1 0 0 0
1 7 0 11 10 15 10
6 17 2 6
0 0 1 0 0 1
7 6 3 7 10 12
5 17 2 5
1 1 1 1 0
17 11 10 6 4
1 1 1 2
0
1

输出样例 #1

3
2
1
0
1
4
0
1
2
1

题意翻译

Petya将会参加一场考试，这场考试从时间点0开始，到T结束。考试中有n道题，分为两种，简单（需要花a时间做完）的题和困难（需要花b时间做完）的题（a <= b），即在时间点x开始做这道题，将会在x+a或x+b时间点完成。现在每道题会在时间点 ti 变成必须完成，Petya可以在0 ~ T任意一个时间点离开，若离开时有必须要完成的题目没有完成，他将会得到0分，否则会得到他完成的题目的分数。求他最大能得到的分数。