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: from collections import deque
  
  N, M = map(int, input().split())
  A = [[] for _ in range(N)]
  
  for i in range(M):
      u, v, s = map(int, input().split())
      u, v = u - 1, v - 1
      A[u].append((v, s))
      A[v].append((u, s))
  
  # up[i] A[0]=tとしたときの A[i] = a + t > 0 <=> t > up[i]
  # dw[i] A[0]=tとしたときの A[i] = a - t > 0 <=> t < dw[i]
  UP = [-1 for _ in range(N)]
  DW = [10**9 + 1 for _ in range(N)]
  UP[0] = 0
  # DW[0] = 0
  
  
  # nodeじゃなくて、edgeを全探索する必要がある気がする。。。
  # bfsすれば良いのか？
  def solve():
      visited = [False for _ in range(N)]
      willSearch = [False for _ in range(N)]
      Q = deque()
      # (node, depth)
      Q.append((0, 0))
      while Q:
          now, depth = Q.pop()
          visited[now] = True
          for nxt, cost in A[now]:
              if depth % 2 == 1:
                  UP[nxt] = max(UP[nxt], DW[now] - cost)
              else:
                  DW[nxt] = min(DW[nxt], UP[now] + cost)
              # 訪問済みなら、エッジはPUSHしなくて良い
              if visited[nxt] or willSearch[nxt]:
                  continue
              Q.append((nxt, depth + 1))
  
  
  solve()
  # print(UP)
  # print(DW)
  up, dw = 0, 10**9
  for x in UP:
      if x >= 0:
          up = max(up, x)
  for x in DW:
      if x <= 10**9:
          dw = min(dw, x)
  
  print(dw - up - 1)
  
  
  """
  1 -(5)-> 2 -(3)-> 3 - (8)-> 4
  1がtだと、2は5-t、　３はt-2, 4は10-t
  
  """
  
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"}]