Allen, Nella's older brother, has a better way of building graphs; he plugs them into his graph generator! The generator takes items as input:

- An initial graph consisting of nodes labeled from to connected by distinct undirected edges of length .
- An array of length , where if nodes labeled are producers and otherwise.
- A positive integer , the number of generation phases.

The generator then begins building the graph, happening in generation phases. In the first phase, the graph is constructed. Then, for every phase after the first, the generator does the following:

For every node that is a producer constructed in the previous phase, construct a copy of and connect node of the copy to with an undirected edge of length .

To estimate the size of the graph constructed after the -th generation phase is over, compute the sum of the lengths of the shortest paths between every pair of nodes.

#### Constraints

is connected.

##### Subtask 1 [20%]

##### Subtask 2 [30%]

##### Subtask 3 [50%]

No additional constraints.

#### Input Specification

The first line contains integers , , and .

The second line contains integers .

The next lines each contain integers and , the labels of the endpoints of the -th edge in . All edges are distinct, and there are no self-loops.

#### Output Specification

Output the sum of the lengths of the shortest paths between every pair of nodes. Since this value may be large, output it modulo .

#### Sample Input

```
2 1 2
1 1
1 2
```

#### Sample Output

`35`

## Comments