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: Accepted)

from collections import defaultdict 
import sys
import heapq

sys.setrecursionlimit(10**8)

#N:頂点数   M:辺数
N,M,s,t = map(int,input().split())


#root[n] -> nからいけるlist
roots = defaultdict(set)

#weight[a] = start -> a のコスト 未探索->-1
weight_yen = [-1 for i in range(N+1)]
weight_snu = [-1 for i in range(N+1)]
weight_yen[s] = 0
weight_snu[t] = 0


for i in range(M):
	u,v,a,b = list(map(int,input().split())) #

	roots[u].add((v,a,b))
	roots[v].add((u,a,b))
		
	
def search_yen (n,w_0): #nから更新 w_0:確定コスト
	global weight_yen
		
	for root in list(roots[n]):
		i = root[0]
		w = w_0 + root[1]
		if weight_yen[i] == -1 or weight_yen[i] > w: #未探索orより小さい
			heapq.heappush(q, [w,i])
			weight_yen[i] = w
			
def search_snu (n,w_0): #nから更新 w_0:確定コスト
	global weight_snu
		
	for root in list(roots[n]):
		i = root[0]
		w = w_0 + root[2]
		if weight_snu[i] == -1 or weight_snu[i] > w: #未探索orより小さい
			heapq.heappush(q, [w,i])
			weight_snu[i] = w

#q = 次に探索する(確定する)もの q[0]=[w,n]
q = [[0,s]]
heapq.heapify(q)
			
while q:
	w,n = heapq.heappop(q)
	search_yen(n,w)
	
heapq.heappush(q, [0,t])
	
while q:
	w,n = heapq.heappop(q)
	search_snu(n,w)
	

finalans = float('inf')
ans_li = []

for i in range(0,N):
	ans = weight_yen[N-i] + weight_snu[N-i]
	finalans = min(finalans, ans)
	ans_li.append(finalans)
	
for i in range(N):
	print(10**15 - ans_li[N-i-1])