Unidentified Destination

(kzzt) Agent B100, a pair of circus performers in loud outfits is moving through the streets of a city. Your mission is to find out where they are going. What we know is that they left from intersection $s$, and that one of the destination candidates is their real destination. They are in a hurry, so they take a shortest route with no detours. Over. (kzzt)

Ugh, the duo (loud outfits and all) is nowhere to be seen. Luckily your nose is as good as a dog's, and it told you that the two passed along the road between intersections $g$ and $h$.

So where on earth is this duo going? Among the destination candidates, find every point such that some shortest route from $s$ to it uses the road between $g$ and $h$.

The first line has the number of test cases $T$ ($1 \le T \le 100$). Each test case looks like this.

• The first line has three integers $n$, $m$, $t$ ($2 \le n \le 2000$, $1 \le m \le 50000$, $1 \le t \le 100$): the number of intersections, roads, and destination candidates.
• The second line has three integers $s$, $g$, $h$ ($1 \le s, g, h \le n$, $g \ne h$). $s$ is where the artists started, and $g$ and $h$ are the two intersections described above.
• Each of the next $m$ lines has three integers $a$, $b$, $d$ ($1 \le a < b \le n$, $1 \le d \le 1000$), meaning a two-way road of length $d$ runs between intersections $a$ and $b$.
• Each of the next $t$ lines has one destination candidate $x$. These $t$ points are distinct and none of them equals $s$.

At most one road directly joins any two intersections. One of the $m$ roads joins $g$ and $h$, and that road lies on a shortest route to at least one of the destination candidates.

For each test case, print on one line the destination candidates that some shortest route from $s$ reaches through the road between $g$ and $h$, in increasing order, separated by single spaces. At least one candidate always qualifies.