AMP is a cute caterpillar living in the SK (Shik Kingdom). As a result of her addiction on placing sticks on the table, she plans to buy a looooooong table to place sticks on. However, instead of buying the looooooongest table, AMP would like to buy a table that has most “shiky" ways to place sticks on.
A placement of sticks is valid if and only if the sum of length of sticks on the table is not greater than the length of table. It's “shiky" if and only if it's valid and it will become invalid if we add any of the remaining sticks. It's quite complicate, right? Well, it's “shiky"! Note that AMP never cares about the order of sticks.
The first line contains an integer T, the number of test cases. There're two integers N; L in first line of each test case. The next line contains N integers, representing the length of each stick.
1<=T<=10
1<=N<=200
<=1<=L<=20000
AMP is such a kind caterpillar that she won't ask you to buy the table. What you need to do is printing out L integers for each test case where the k-th integer represents the number of "shiky" ways to place sticks on a k unit long table.
Since the number maybe very LARGE, please output that number modulo 514514514.