# Single source shortest path, time table

## Input

The input consists of several test cases. Each test case starts with a line with four non-negative integers, $1 \le n \le 10\, 000$, $0 \le m \le 20\, 000$, $1 \le q \le 100$ 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 five (space-separated) integers $u$, $v$, $t_{0}$, $P$ and $d$ indicating that there is an edge from $u$ to $v$ in the graph which can be traversed at time $t_{0} + t \cdot P$ for all nonnegative integers $t$, and that it takes $d$ time units to traverse the edge. You may assume $0 \le t_0, P, d \le 1000$.

For instance, the edge `3 8 15 10 5`
indicates that at time $15, 25,
35, 45, \ldots $, we can travel from node $3$ to node $8$ in $5$ time units. Note that it is
possible to stand still at a node, to wait for an edge to
become available. Also, note that if $P = 0$, the edge can be used only at
time $t_{0}$ and never
again.

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
time to reach the node queried, assuming we start in node
$s$ at time $0$, or the word “`Impossible`” if there is no path from
$s$ to that node. For
clarity, the sample output has a blank line between the output
for different cases.

Sample Input 1 | Sample Output 1 |
---|---|

4 4 4 0 0 1 15 10 5 1 2 15 10 5 0 2 5 5 30 3 0 0 1 1 0 1 2 3 2 1 1 0 0 1 100 0 5 1 0 0 0 0 |
0 20 30 Impossible 105 |