output_description: Print n lines. In the i-th line, print the maximum amount of snuuk that
  Kenkoooo has when he reaches City t if he goes on a trip from City s to City t
  after i-1 years.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      n m s t
      u_1 v_1 a_1 b_1
      :
      u_m v_m a_m b_m
attempt: from heapq import *
  
  INF = 10**15
  
  def djikstra(G,s,d):
      #d = [0]*V
      que = []
      d[s] = 0
      visited = [False] * V
      heappush(que,(0,s))
      while(len(que)!=0):
          c,v = heappop(que)
          if visited[v]:
              continue
          visited[v] = True
          for i in range(len(G[v])):
              e = G[v][i]
              if visited[e[0]]:
                  continue
              if d[e[0]] > d[v] + e[1]:
                  d[e[0]] = d[v] + e[1]
                  heappush(que,(d[e[0]],e[0]))
  
  
  n,m,s,t = map(int,input().split())
  V = n
  Ga = [[] for i in range(n)]
  Gb = [[] for i in range(n)]
  for i in range(m):
      u,v,a,b = map(int,input().split())
      Ga[u-1].append((v-1,a))
      Ga[v-1].append((u-1,a))
      Gb[u-1].append((v-1,b))
      Gb[v-1].append((u-1,b))
  
  S = [INF]*V
  T = [INF]*V
  djikstra(Ga,s-1,S)
  djikstra(Gb,t-1,T)
  M = [0]*n
  for i in range(n):
  M[i] = INF-S[i]-T[i]
  ans = [0]*n
  ans[n-1] = M[n-1]
  for i in range(n-2,-1,-1):
      ans[i] = max(ans[i+1],M[i])
  
  for i in range(n):
      print(ans[i])
  
problem_description: Statement
  
  Kenkoooo is planning a trip in Republic of Snuke. In this country, there are n
  cities and m trains running. The cities are numbered 1 through n, and the i-th
  train connects City u_i and v_i bidirectionally. Any city can be reached from
  any city by changing trains.
  
  Two currencies are used in the country: yen and snuuk. Any train fare can be
  paid by both yen and snuuk. The fare of the i-th train is a_i yen if paid in
  yen, and b_i snuuk if paid in snuuk.
  
  In a city with a money exchange office, you can change 1 yen into 1 snuuk.
  However, when you do a money exchange, you have to change all your yen into
  snuuk. That is, if Kenkoooo does a money exchange when he has X yen, he will
  then have X snuuk. Currently, there is a money exchange office in every city,
  but the office in City i will shut down in i years and can never be used in
  and after that year.
  
  Kenkoooo is planning to depart City s with 10^{15} yen in his pocket and head
  for City t, and change his yen into snuuk in some city while traveling. It is
  acceptable to do the exchange in City s or City t.
  
  Kenkoooo would like to have as much snuuk as possible when he reaches City t
  by making the optimal choices for the route to travel and the city to do the
  exchange. For each i=0,...,n-1, find the maximum amount of snuuk that Kenkoooo
  has when he reaches City t if he goes on a trip from City s to City t after i
  years. You can assume that the trip finishes within the year.
samples: [{"input": "4 3 2 3\n    1 4 1 100\n    1 2 1 10\n    1 3 20 1", "output": "999999999999998\n    999999999999989\n    999999999999979\n    999999999999897\n    \n\nAfter 0 years, it is optimal to do the exchange in City 1.  \nAfter 1 years, it is optimal to do the exchange in City 2.  \nNote that City 1 can still be visited even after the exchange office is\nclosed. Also note that, if it was allowed to keep 1 yen when do the exchange\nin City 2 and change the remaining yen into snuuk, we could reach City 3 with\n999999999999998 snuuk, but this is NOT allowed.  \nAfter 2 years, it is optimal to do the exchange in City 3.  \nAfter 3 years, it is optimal to do the exchange in City 4. Note that the same\ntrain can be used multiple times.\n\n* * *"}, {"input": "8 12 3 8\n    2 8 685087149 857180777\n    6 7 298270585 209942236\n    2 4 346080035 234079976\n    2 5 131857300 22507157\n    4 8 30723332 173476334\n    2 6 480845267 448565596\n    1 4 181424400 548830121\n    4 5 57429995 195056405\n    7 8 160277628 479932440\n    1 6 475692952 203530153\n    3 5 336869679 160714712\n    2 7 389775999 199123879", "output": "999999574976994\n    999999574976994\n    999999574976994\n    999999574976994\n    999999574976994\n    999999574976994\n    999999574976994\n    999999574976994"}]