Fatima commutes from KTH to home by subway every day. Today
Robert decided to surprise Fatima by baking cookies and
bringing them to an intermediate station. Fatima does not
always take the same route home, because she loves to admire
the artwork inside different stations in Stockholm. However,
she always optimizes her travel by taking the shortest route.
Can you tell Robert which station he should go to in order to
surely intercept Fatima?
Input
The first line contains two integers $N$ and $M$, $1
\leq N,M \leq 100\, 000$, where $N$ is the number of subway stations
and $M$ is the number of
subway links. $M$ lines
follow, each with three integers $u$, $v$, $w$, $0
\leq u,v < N$, $0 <
w \leq 1\, 000\, 000\, 000$, meaning that there is a
oneway link from $u$ to
$v$ that takes
$w$ seconds to complete.
Note that different subway lines may serve the same route.
The last line contains two integers $s$ and $t$, $0
\leq s,t < N$ the number of the station closest to
KTH and closest to home, respectively. It is possible to reach
$t$ from $s$.
Output
A space separated list of all the station numbers
$u$ such that all shortest
paths from $s$ to
$t$ pass through
$u$, in increasing
order.
Sample Input 1 
Sample Output 1 
4 4
0 1 100
0 2 100
1 3 100
2 3 100
0 3

0 3

Sample Input 2 
Sample Output 2 
7 8
0 1 100
0 2 100
1 3 100
2 3 100
3 4 100
3 5 100
4 6 100
5 6 100
0 6

0 3 6
