Problem:
Score : 400 points

Problem 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.

Constraints

2 \leq n \leq 10^5

1 \leq m \leq 10^5

1 \leq s,t \leq n

s \neq t

1 \leq u_i < v_i \leq n

1 \leq a_i,b_i \leq 10^9

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

Any city can be reached from any city by changing trains.

All values in input are integers.

Input

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

Output

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.

Sample Input 1

4 3 2 3
1 4 1 100
1 2 1 10
1 3 20 1

Sample Output 1

999999999999998
999999999999989
999999999999979
999999999999897

After 0 years, it is optimal to do the exchange in City 1.

After 1 years, it is optimal to do the exchange in City 2.

Note that City 1 can still be visited even after the exchange office is closed.
Also note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.

After 2 years, it is optimal to do the exchange in City 3.

After 3 years, it is optimal to do the exchange in City 4.
Note that the same train can be used multiple times.

Sample Input 2

8 12 3 8
2 8 685087149 857180777
6 7 298270585 209942236
2 4 346080035 234079976
2 5 131857300 22507157
4 8 30723332 173476334
2 6 480845267 448565596
1 4 181424400 548830121
4 5 57429995 195056405
7 8 160277628 479932440
1 6 475692952 203530153
3 5 336869679 160714712
2 7 389775999 199123879

Sample Output 2

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import defaultdict

n, m, s, t = map(int, input().split())
X = [tuple(map(int, input().split())) for _ in range(m)]
y = 10 ** 15


class DijkstraAlgorithm(object):
    def __init__(self, edges, directed=False, start_node=0):
        self.nodes = self.edge_to_node(edges, directed)
        self.nodes[start_node]['cost'] = 0

    def run(self):
        while True:
            # 確定ノードを探索
            doneNode = None
            for node in self.nodes.values():
                if node['done'] or node['cost'] < 0:
                    continue
                if doneNode is None or node['cost'] < doneNode['cost']:
                    doneNode = node
            if doneNode is None:
                break

            doneNode['done'] = True

            # 接続先ノードの情報更新
            for i in range(len(doneNode['edges_to'])):
                to = doneNode['edges_to'][i]
                cost = doneNode['cost'] + doneNode['edges_cost'][i]
                self.nodes[to]['cost'] = min(self.nodes[to]['cost'], cost)

    def shortest_distance(self, goal_node):
        self.run()
        return self.nodes[goal_node]['cost']

    def edge_to_node(self, edges, directed):
        nodes = defaultdict(
            lambda: {'edges_to': [], 'edges_cost': [], 'done': False, 'cost': float('inf')})
        for i, j, k in edges:
            nodes[i]['edges_to'].append(j)
            nodes[i]['edges_cost'].append(k)

            if not directed:
                nodes[j]['edges_to'].append(i)
                nodes[j]['edges_cost'].append(k)
        return nodes


cost = [0] * n

edges = [(u, v, a) for u, v, a, b in X]
da = DijkstraAlgorithm(edges, start_node=s)
for i in range(1, n + 1):
    cost[i - 1] += da.shortest_distance(i)

edges = [(u, v, b) for u, v, a, b in X]
da = DijkstraAlgorithm(edges, start_node=t)
for i in range(1, n + 1):
    cost[i - 1] += da.shortest_distance(i)

for i in range(n):
    print(y - min(cost[i:]))