Alien invasion began, and scary maneating aliens are
establishing their bases all over the country. You are only
safe on the places that are sufficiently far away from all
current alien bases. You need to quickly write a program to
help you determine where to move.
Input
The input contains at most $25$ instances, each of them
consisting of several lines. The first line of each instance
contains integers $N$
($1 \leq N \leq 10\ 000$),
$M$ ($0 \leq M \leq 100\ 000$),
$A$ ($0 \leq A \leq N$) and $K$ ($1
\leq K \leq 100$) separated by spaces, giving the number
of towns in the country, the number of roads between them, the
number of bases that the aliens are going to build, and the
minimum safe distance from alien bases, respectively. The towns
are assigned numbers $1, \ldots ,
N$.
The following $M$ lines
describe the roads; each of them contains integers $T_1$, $T_2$ ($1 \leq T_1 < T_2 \leq N$) and
$D$ ($1 \leq D \leq 100$) separated by
spaces, where $D$ is the
length of the road between towns $T_1$ and $T_2$. There is at most one direct
road between any two towns. All roads can be used in both
directions.
The following $A$ lines
describe the positions of alien bases; the $i$th of them contains the number
$B_ i$ ($1 \leq B_ i \leq N$) of the town
where the aliens build their $i$th base.
The last instance is followed by a line containing four
zeros.
Output
The output for each input instance consists of $A$ lines. On $i$th line, write the number of towns
that are safe after the aliens build their $i$th base. The town is safe if its
distance from any of the towns $B_1, B_2, \ldots , B_ i$ is at least
$K$.
Print one empty line after each instance.
Sample Input 1 
Sample Output 1 
7 6 3 3
1 2 1
1 3 1
2 5 1
3 6 1
1 4 1
4 7 2
2
1
4
1 0 1 1
1
0 0 0 0

2
1
0
0
