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: import sys
  
  sys.setrecursionlimit(100000)
  
  
  def dfs1(v, p):
      val = 1
      pre_mul = [1]
      rev_mul = []
      for c in links[v]:
          if c == p:
              pre_mul.append(val)
              rev_mul.append(1)
              continue
          res = 1 + dfs1(c, v)
          val *= res
          val %= m
          pre_mul.append(val)
          rev_mul.append(res)
      dp[v] = val
      for i in range(len(rev_mul) - 2, -1, -1):
          rev_mul[i] *= rev_mul[i + 1]
          rev_mul[i] %= m
      rev_mul.append(1)
      pre_muls[v] = [pre_mul, rev_mul]
      return val
  
  
  def dfs2(v, p, a):
      dp[v] = dp[v] * a % m
      pmv = pre_muls[v]
      for i, c in enumerate(links[v]):
          if c == p:
              continue
          pmc = pmv[0][i] * pmv[1][i + 1] % m
          pmc = pmc * a % m
          dfs2(c, v, pmc + 1)
  
  
  n, m = map(int, input().split())
  links = [[] for _ in range(n)]
  dp = [0 for _ in range(n)]
  pre_muls = [None for _ in range(n)]
  for line in sys.stdin.readlines():
      x, y = map(int, line.split())
      x -= 1
      y -= 1
      links[x].append(y)
      links[y].append(x)
  dfs1(0, None)
  dfs2(0, None, 1)
  print("\n".join(map(str, dp)))
  
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."}]