Score : 100 points
There is a tree with N vertices, numbered 1, 2, \ldots, N. For each i (1 \leq i \leq N - 1), the i-th edge connects Vertex x_i and y_i.
Taro has decided to paint each vertex in white or black, so that any black vertex can be reached from any other black vertex by passing through only black vertices.
You are given a positive integer M. For each v (1 \leq v \leq N), answer the following question:
Input is given from Standard Input in the following format:
N M x_1 y_1 x_2 y_2 : x_{N - 1} y_{N - 1}
Print N lines. The v-th (1 \leq v \leq N) line should contain the answer to the following question:
3 100 1 2 2 3
3 4 3
There are seven ways to paint the vertices, as shown in the figure below. Among them, there are three ways such that Vertex 1 is black, four ways such that Vertex 2 is black and three ways such that Vertex 3 is black.
4 100 1 2 1 3 1 4
8 5 5 5
1 100
1
10 2 8 5 10 8 6 5 1 5 4 8 2 10 3 6 9 2 1 7
0 0 1 1 1 0 1 0 1 1
Be sure to print the answers modulo M.