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 PyPy3 (2.4.0) (judge verdict: Accepted)

import heapq

# s:始点, path[from]:[[cost,to]...] 隣接リスト
def dijkstra(s,path):
    inf = float('inf')
    n = len(path)

    # 距離をinfで初期化
    d = [inf for i in range(n)]
    d[s] = 0

    # sへの距離は0
    q = [(0,s)]
    heapq.heapify(q)

    # 距離が最小の頂点から更新していけば良い
    while q:
        c,p = heapq.heappop(q)

        # 頂点pまでの距離がheap内のpまでの距離より小さい場合、continue
        if d[p]<c:
            continue

        # 頂点pから伸びる、全ての辺の距離を確認
        for cost,to in path[p]:
            # 頂点pから行ける頂点の距離がpまでの距離とpからの距離の和より小さい場合 -> 距離を更新し、heapに追加
            if d[to] > d[p] + cost:
                d[to] = d[p]+cost
                heapq.heappush(q,(d[to], to))
    return d


n,m,s,t = map(int, input().split())
s-=1
t-=1
train = [list(map(int, input().split())) for i in range(m)]

yen = [[] for i in range(n)]
snuke = [[] for i in range(n)]

for i in range(m):
    u,v,a,b = train[i]
    u-=1
    v-=1
    yen[u].append([a,v])
    yen[v].append([a,u])
    snuke[u].append([b,v])
    snuke[v].append([b,u])

from_s = dijkstra(s,yen)
to_t = dijkstra(t,snuke)

left = [0 for i in range(n)]
left[-1]=from_s[n-1]+to_t[n-1]


for i in range(1,n):
    left[-i-1]=min(left[-i],from_s[-i-1]+to_t[-i-1])

for i in range(n):
    print(10**15-left[i])