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: Runtime Error)

import sys
import numpy as np
from scipy.sparse.csgraph import dijkstra
from scipy.sparse import coo_matrix

read = sys.stdin.read
readline = sys.stdin.readline

n, m, s, t, *uvab = map(int, read().split())
if n == m == 10 ** 5:
    from heapq import heappush, heappop

    N, M, S, T = n, m, s, t
    graph = [[] for _ in range(N + 1)]
    for u, v, a, b in zip(*[iter(uvab)] * 4):
        graph[u].append((v, a, b))
        graph[v].append((u, a, b))


    def dijkstra(start, mode):
        INF = 10 ** 15
        dist = [INF] * (N + 1)
        dist[start] = 0
        q = [(0, start)]
        while q:
            d, v = heappop(q)
            if dist[v] < d:
                continue
            for w, *a in graph[v]:
                d1 = d + a[mode]
                if dist[w] > d1:
                    dist[w] = d1
                    heappush(q, (d1, w))
        return dist


    d1 = np.array(dijkstra(S, 0))
    d2 = np.array(dijkstra(T, 1))

    d1 += d2
    answer = 10 ** 15 - np.minimum.accumulate(d1[::-1])[::-1][1:]
    print('\n'.join(answer.astype(str)))
    exit()
s -= 1
t -= 1
u = np.array(uvab[::4], np.int64) - 1
v = np.array(uvab[1::4], np.int64) - 1
a = np.array(uvab[2::4], np.int64)
b = np.array(uvab[3::4], np.int64)

yen_matrix = coo_matrix((a, (u, v)), shape=(n, n), dtype=float_)
snuuk_matrix = coo_matrix((b, (u, v)), shape=(n, n))

yen = dijkstra(yen_matrix, directed=False, indices=s)
snuuk = dijkstra(snuuk_matrix, directed=False, indices=t)

costs = (yen + snuuk).astype(int)
answer = 10 ** 15 - np.minimum.accumulate(costs[::-1])[::-1]
print(*answer.tolist(), sep='\n')