JMU F17 Week 9

Start

2017-10-30 22:00 CET

JMU F17 Week 9

End

2017-11-06 22:00 CET
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Problem F
Single source shortest path, non-negative weights

Input

The input consists of several test cases. Each test case starts with a line with four non-negative integers, $1 \le n \le 10\, 000$, $0 \le m \le 30\, 000$, $1 \le q \le 100$ and $0 \le s < n$, separated by single spaces, where $n$ is the numbers of nodes in the graph, $m$ the number of edges, $q$ the number of queries and $s$ the index of the starting node. Nodes are numbered from $0$ to $n-1$. Then follow $m$ lines, each line consisting of three (space-separated) integers $u$, $v$ and $w$ indicating that there is an edge from $u$ to $v$ in the graph with weight $0 \le w \le 1000$. Then follow $q$ lines of queries, each consisting of a single non-negative integer, asking for the minimum distance from node $s$ to the node number given on the query line.

Input will be terminated by a line containing four zeros, this line should not be processed.

Output

For each query, output a single line containing the minimum distance from node $s$ to the node specified in the query, or the word “Impossible” if there is no path from $s$ to that node. Print a blank line after each test case.

Sample Input 1 Sample Output 1
4 3 4 0
0 1 2
1 2 2
3 0 2
0
1
2
3
2 1 1 0
0 1 100
1
0 0 0 0
0
2
4
Impossible

100