Problem Description: 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