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
  from collections import deque
  
  input = sys.stdin.readline
  sys.setrecursionlimit(10**9)
  
  N, mod = map(int, input().split())
  EDGE = [list(map(int, input().split())) for i in range(N - 1)]
  
  if N == 1:
      print(1)
      sys.exit()
  
  EDGELIST = [[] for i in range(N + 1)]
  for x, y in EDGE:
      EDGELIST[x].append(y)
      EDGELIST[y].append(x)
  
  SCORELIST = [[-1] * len(EDGELIST[i]) for i in range(N + 1)]
  PRODLIST = [[-1] * len(EDGELIST[i]) for i in range(N + 1)]
  PRODLIST_rev = [[-1] * len(EDGELIST[i]) for i in range(N + 1)]
  EDICT = dict()
  
  for i in range(1, N + 1):
      for j in range(len(EDGELIST[i])):
          EDICT[(i, EDGELIST[i][j])] = j
  
  
  def dp(x, y):
      if SCORELIST[y][EDICT[(y, x)]] != -1:
          return SCORELIST[y][EDICT[(y, x)]]
  
      ANS = 1
      for to in EDGELIST[x]:
          if to == y:
              continue
          ANS = ANS * dp(to, x) % mod
  
      SCORELIST[y][EDICT[(y, x)]] = ANS + 1
      return ANS + 1
  
  
  def dp2(x, y):
      if PRODLIST[x][0] == -1:
          PRODLIST[x][0] = (SCORELIST[x][0]) % mod
          for i in range(1, len(EDGELIST[x])):
              PRODLIST[x][i] = PRODLIST[x][i - 1] * SCORELIST[x][i] % mod
  
          PRODLIST_rev[x][-1] = SCORELIST[x][-1]
          for i in range(len(EDGELIST[x]) - 2, -1, -1):
              PRODLIST_rev[x][i] = PRODLIST_rev[x][i + 1] * SCORELIST[x][i] % mod
  
      if len(EDGELIST[x]) == 1:
          ANS = 1
      elif EDICT[(x, y)] == 0:
          ANS = PRODLIST_rev[x][1]
      elif EDICT[(x, y)] == len(EDGELIST[x]) - 1:
          ANS = PRODLIST[x][EDICT[(x, y)] - 1]
      else:
          ANS = PRODLIST[x][EDICT[(x, y)] - 1] * PRODLIST_rev[x][EDICT[(x, y)] + 1] % mod
  
      SCORELIST[y][EDICT[(y, x)]] = ANS + 1
  
  
  for to in EDGELIST[1]:
      dp(to, 1)
  
  QUE = deque([1])
  check = [0] * (N + 1)
  
  while QUE:
      x = QUE.pop()
      if check[x] == 1:
          continue
      for to in EDGELIST[x]:
          if check[x] == 0 or check[to] == 0:
              dp2(x, to)
              QUE.append(to)
      check[x] = 1
  
  for i in range(1, N + 1):
      print(PRODLIST[i][-1])
  
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."}]