Problem:
Score : 600 points

Problem 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.

Constraints

2 \leq n \leq 10^5

1 \leq m \leq 10^5

1 \leq u_i < v_i \leq n

2 \leq s_i \leq 10^9

If i\neq j, then u_i \neq u_j or v_i \neq v_j.

The graph is connected.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m
u_1 v_1 s_1
:
u_m v_m s_m

Output

Print the number of ways to write positive integers in the vertices so that the condition is satisfied.

Sample Input 1

3 3
1 2 3
2 3 5
1 3 4

Sample Output 1

1

The condition will be satisfied if we write 1,2 and 3 in vertices 1,2 and 3, respectively.
There is no other way to satisfy the condition, so the answer is 1.

Sample Input 2

4 3
1 2 6
2 3 7
3 4 5

Sample Output 2

3

Let a,b,c and d be the numbers to write in vertices 1,2,3 and 4, respectively.
There are three quadruples (a,b,c,d) that satisfy the condition:

(a,b,c,d)=(1,5,2,3)

(a,b,c,d)=(2,4,3,2)

(a,b,c,d)=(3,3,4,1)

Sample Input 3

8 7
1 2 1000000000
2 3 2
3 4 1000000000
4 5 2
5 6 1000000000
6 7 2
7 8 1000000000

Sample Output 3

0

Solution in Python (3.8.2) (judge verdict: Wrong Answer)

import sys
sys.setrecursionlimit(10**9)
n,m=map(int,input().split())

graph=[[] for _ in range(n+1)]
for _ in range(m):
  u,v,s=map(int,input().split())
  graph[u].append((v,s))
  graph[v].append((u,s))
  
def has_cycle(u,par):
  visited[u]=True
  
  ret=False
  for v,w in graph[u]:
    if v==par:
      continue     
    if visited[v]:
      return True
    else:
      if has_cycle(v,u):
        ret=True
      
  return ret

visited=[False]*(n+1)
cyclic=has_cycle(1,0)

min_even=float("inf")
min_odd=float("inf")
def add_score_acyclic(u,par,weight,depth):
  visited[u]=True
  point_list[u]=weight-point_list[par]
  if depth%2==0:
    global min_even
    min_even=min(min_even,point_list[u])
  else:
    global min_odd
    min_odd=min(min_odd,point_list[u])
  
  for v,w in graph[u]:
    if v==par:
      continue     
    add_score_acyclic(v,u,w,depth+1)

if cyclic:
  #temp
  print(1)
else:
  point_list=[0]*(n+1)
  add_score_acyclic(1,0,0,0)
  
  #print(point_list)
  #print(min_even,min_odd)
  print(max(0,min_even+min_odd-1))