B"Kawashiro Nitori is a girl who loves competitive programming. One day she found a rooted tree consisting of n vertices. The root is vertex 1 . As an advanced problem setter, she quickly thought of a problem. Kawashiro Nitori has a vertex set U= {1,2, ldots,n } . She's going to play a game with the tree and the set. In each operation, she will choose a vertex set T , where T is a partial virtual tree of U , and change U into T . A vertex set S_1 is a partial virtual tree of a vertex set S_2 , if S_1 is a subset of S_2 , S_1 neq S_2 , and for all pairs of vertices i and j in S_1 , operatorname{LCA}(i,j) is in S_1 , where operatorname{LCA}(x,y) denotes the lowest common ancestor of vertices x and y on the tree. Note that a vertex set can have many different partial virtual trees. Kawashiro Nitori wants to know for each possible k , if she performs the operation exactly k times, in how many ways she can make U= {1 } in the end? Two ways are considered different if there exists an integer z ( 1 <= z <= k ) such that after z operations the sets U are different. Since the answer could be very large, you need to find it modulo p . It's guaranteed that p is a prime number. The first line contains two integers n and p ( 2 <= n <= 2000 , 10^8 + 7 <= p <= 10^9+9 ). It's guaranteed that p is a prime number. Each of the next n-1 lines contains two integers u_i , v_i ( 1 <= q u_i, v_i <= q n ), representing an edge between u_i and v_i . It is guaranteed that the given edges form a tree. The only line contains n-1 integers -- the answer modulo p for k=1,2, ldots,n-1 . In the first test case, when k=1 , the only possible way is: When k=2 , there are 6 possible ways: When k=3 , there are 6 possible "...