output_description: Print N lines. The v-th (1 \leq v \leq N) line should contain the answer to
  the following question:
  
    * Assuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.
  
  * * *
input_description: 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}
attempt: # 参考 -> https://atcoder.jp/contests/dp/submissions/8271798
  
  import itertools
  import sys
  
  input = sys.stdin.readline
  
  N, MOD = map(int, input().split())
  XY = [list(map(int, input().split())) for i in range(N - 1)]
  prod = lambda x, y: x * y % MOD
  
  tree = [[] for i in range(N)]
  for x, y in XY:
      tree[x - 1].append(y - 1)
      tree[y - 1].append(x - 1)
  
  root = 0
  parent = [-1] * (N + 1)
  order = []
  stack = [root]
  while stack:
      node = stack.pop()
      order.append(node)
      for child in tree[node]:
          if child == parent[node]:
              continue
          parent[child] = node
          stack.append(child)
  
  # dp_down[i] : 頂点iを黒く塗ったときの子側の塗り方
  dp_down = [0] * N
  for node in order[::-1]:  # 葉から根に向かって伝搬させる
      res = 1
      for child in tree[node]:
          res *= dp_down[child] + 1
          res %= MOD
      dp_down[node] = res
  
  # dp_up[i] : 頂点iを黒く塗ったときの親側の塗り方
  dp_up = [1] * N
  for node in order:  # 根から葉に向かって伝搬させる
      par = parent[node]
      arr = [dp_down[c] + 1 if c != par else dp_up[node] for c in tree[node]]
      # それぞれの子(=c)について、自身を根とする下側の部分木を除いた積
      left = [1] + list(itertools.accumulate(arr, prod))[:-1]
      right = list(itertools.accumulate(reversed(arr), prod))[-2::-1] + [1]
      upper_cases = [l * r % MOD for l, r in zip(left, right)]
      for c, res in zip(tree[node], upper_cases):
          if c != par:
              dp_up[c] = res + 1  # (+1 : cより上側が全て白である場合を足し合わせる)
  
  ans = [d * u % MOD for d, u in zip(dp_down, dp_up)]
  print(*ans, sep="\n")
  
problem_description: Statement
  
  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:
  
    * Assuming that Vertex v has to be black, find the number of ways in which the vertices can be painted, modulo M.
samples: [{"input": "3 100\n    1 2\n    2 3", "output": "3\n    4\n    3\n    \n\nThere are seven ways to paint the vertices, as shown in the figure below.\nAmong them, there are three ways such that Vertex 1 is black, four ways such\nthat Vertex 2 is black and three ways such that Vertex 3 is black.\n\n![](https://img.atcoder.jp/dp/subtree_0_muffet.png)\n\n* * *"}, {"input": "4 100\n    1 2\n    1 3\n    1 4", "output": "8\n    5\n    5\n    5\n    \n\n* * *"}, {"input": "1 100", "output": "1\n    \n\n* * *"}, {"input": "10 2\n    8 5\n    10 8\n    6 5\n    1 5\n    4 8\n    2 10\n    3 6\n    9 2\n    1 7", "output": "0\n    0\n    1\n    1\n    1\n    0\n    1\n    0\n    1\n    1\n    \n\nBe sure to print the answers modulo M."}]