output_description: Print the number of ways to write positive integers in the vertices so that
  the condition is satisfied.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      n m
      u_1 v_1 s_1
      :
      u_m v_m s_m
attempt: import sys
  
  sys.setrecursionlimit(10**8)
  
  
  def dfs(v):
      checked[v] = 1
      for u, s in g[v]:
          if checked[u] == 1:
              continue
          vl, vr = lrs[v]
          if vl == 1 and vr == 0:
              lrs[u] = (1, 0)
              continue
          ul = s - vr
          if ul <= 0:
              ul = 1
          ur = s - vl
          if ur <= 0:
              ur = 0
          lrs[u] = (ul, ur)
          dfs(u)
  
  
  n, m = map(int, input().split())
  arr = [list(map(int, input().split())) for _ in range(m)]
  g = [[] for _ in range(n + 1)]
  for u, v, s in arr:
      g[u].append((v, s))
      g[v].append((u, s))
  lrs = [(0, 0) for _ in range(n + 1)]
  lrs[1] = (1, g[1][0][1] - 1)
  checked = [0] * (n + 1)
  dfs(1)
  for u, v, s in arr:
      ul, ur = lrs[u]
      vl, vr = lrs[v]
      nul = s - vr
      if nul <= 0:
          nul = 1
      nur = s - vl
      if nur <= 0:
          nur = 0
      nvl = s - ur
      if nvl <= 0:
          nvl = 1
      nvr = s - ul
      if nvr <= 0:
          nvr = 0
      lrs[u] = (max(ul, nul), min(ur, nur))
      lrs[v] = (max(vl, nvl), min(vr, nvr))
  ans = 10**18
  for l, r in lrs:
      if l == 0 and r == 0:
          continue
      ans = min(ans, (r - l + 1))
  if ans > 0:
      print(ans)
  else:
      print(0)
  
problem_description: Statement
  
  Kenkoooo found a simple connected graph. The vertices are numbered 1 through
  n. The i-th edge connects Vertex u_i and v_i, and has a fixed integer s_i.
  
  Kenkoooo is trying to write a _positive integer_ in each vertex so that the
  following condition is satisfied:
  
    * For every edge i, the sum of the positive integers written in Vertex u_i and v_i is equal to s_i.
  
  Find the number of such ways to write positive integers in the vertices.
samples: [{"input": "3 3\n    1 2 3\n    2 3 5\n    1 3 4", "output": "1\n    \n\nThe condition will be satisfied if we write 1,2 and 3 in vertices 1,2 and 3,\nrespectively. There is no other way to satisfy the condition, so the answer is\n1.\n\n* * *"}, {"input": "4 3\n    1 2 6\n    2 3 7\n    3 4 5", "output": "3\n    \n\nLet a,b,c and d be the numbers to write in vertices 1,2,3 and 4, respectively.\nThere are three quadruples (a,b,c,d) that satisfy the condition:\n\n  * (a,b,c,d)=(1,5,2,3)\n  * (a,b,c,d)=(2,4,3,2)\n  * (a,b,c,d)=(3,3,4,1)\n\n* * *"}, {"input": "8 7\n    1 2 1000000000\n    2 3 2\n    3 4 1000000000\n    4 5 2\n    5 6 1000000000\n    6 7 2\n    7 8 1000000000", "output": "0"}]