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: #!/usr/bin python3
  # -*- coding: utf-8 -*-
  
  # 有向グラフで優先度付きキューで探索
  
  from heapq import heapify, heappop, heappush, heappushpop
  
  INF = float("inf")
  
  
  def dijkstra(s, n, g):
      seen = [False] * n
      cost = [INF] * n
      cost[s] = 0  # スタートはコスト0
      next_q = [(0, s)]
      heapify(next_q)
      while len(next_q) > 0:
          c, i = heappop(next_q)
          if cost[i] < c:
              continue
          for nedge, ncost in g[i]:
              nc = cost[i] + ncost
              if cost[nedge] > nc:
                  cost[nedge] = nc
                  heappush(next_q, (nc, nedge))
      return cost
  
  
  def main():
      N, M, S, T = map(int, input().split())
      graph_F = [[] for _ in range(N)]
      graph_R = [[] for _ in range(N)]
      # リストの作成
      for i in range(M):
          a, b, c, d = map(int, input().split())
          a -= 1
          b -= 1
          graph_F[a].append((b, c))
          graph_F[b].append((a, c))
          graph_R[a].append((b, d))
          graph_R[b].append((a, d))
  
      F = dijkstra(S - 1, N, graph_F)
      R = dijkstra(T - 1, N, graph_R)
  
      ret = [i + j for (i, j) in zip(F, R)]
      X = 10**15
      for r in range(N - 2, -1, -1):
          ret[r] = min(ret[r + 1], ret[r])
      for r in ret:
          print(X - r)
  
  
  if __name__ == "__main__":
      main()
  
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"}]