C1. Nauuo and Pictures (easy version)time limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe only difference between easy and hard versions is constraints.Nauuo is a girl who loves random picture websites.One day she made a random picture website by herself which includes n pictures.When Nauuo visits the website, she sees exactly one picture. The website does not display each picture with equal probability. The i-th picture has a non-negative weight w_i, and the probability of the i-th picture being displayed is \frac{w_i}{\sum_{j=1}^nw_j}. That is to say, the probability of a picture to be displayed is proportional to its weight.However, Nauuo discovered that some pictures she does not like were displayed too often. To solve this problem, she came up with a great idea: when she saw a picture she likes, she would add 1 to its weight; otherwise, she would subtract 1 from its weight.Nauuo will visit the website m times. She wants to know the expected weight of each picture after all the m visits modulo 998244353. Can you help her?The expected weight of the i-th picture can be denoted by \frac {q_i} {p_i} where \gcd(p_i,q_i)=1, you need to print an integer r_i satisfying 0\le r_i<998244353 and r_i\cdot p_i\equiv q_i\pmod{998244353}. It can be proved that such r_i exists and is unique.InputThe first line contains two integers n and m (1\le n\le 50, 1\le m\le 50) — the number of pictures and the number of visits to the website.The second line contains n integers a_1,a_2,\ldots,a_n (a_i is either 0 or 1) — if a_i=0 , Nauuo does not like the i-th picture; otherwise Nauuo likes the i-th picture. It is guaranteed that there is at least one picture which Nauuo likes.The third line contains n integers w_1,w_2,\ldots,w_n (1\le w_i\le50) — the initial weights of the pictures.OutputThe output contains n integers r_1,r_2,\ldots,r_n — the expected weights modulo 998244353.ExamplesInput
2 1
0 1
2 1
Output
332748119
332748119
Input
1 2
1
1
Output
3
Input
3 3
0 1 1
4 3 5
Output
160955686
185138929
974061117
NoteIn the first example, if the only visit shows the first picture with a probability of \frac 2 3, the final weights are (1,1); if the only visit shows the second picture with a probability of \frac1 3, the final weights are (2,2).So, both expected weights are \frac2 3\cdot 1+\frac 1 3\cdot 2=\frac4 3 .Because 332748119\cdot 3\equiv 4\pmod{998244353}, you need to print 332748119 instead of \frac4 3 or 1.3333333333.In the second example, there is only one picture which Nauuo likes, so every time Nauuo visits the website, w_1 will be increased by 1.So, the expected weight is 1+2=3.Nauuo is very naughty so she didn't give you any hint of the third example.
2 1
0 1
2 1

332748119 332748119 
['dp', 'probabilities', '*2300']