A kingdom has *n* cities numbered 1 to *n*, and some bidirectional roads connecting cities. The capital is always city 1.

After a war, all the roads of the kingdom are destroyed. The king wants to rebuild some of the roads to connect the cities, but unfortunately, the kingdom is running out of money. The total cost of rebuilding roads should not exceed *K*.

Given the list of *m* roads that can be rebuilt (other roads are severely damaged and cannot be rebuilt), the king decided to maximize the total population in the capital and all other cities that are connected (directly or indirectly) with the capital (we call it "accessible population"), can you help him?

The first line of input contains a single integer *T** *(*T*<=20), the number of test cases. Each test case begins with three integers *n*(4<=*n*<=16), *m*(1<=*m*<=100) and *K*(1<=*K*<=100,000). The second line contains *n* positive integers *p** _{i}* (1<=

For each test case, print the maximal accessible population.

```
2
4 6 6
500 400 300 200
1 2 4
1 3 3
1 4 2
4 3 5
2 4 6
3 2 7
4 6 5
500 400 300 200
1 2 4
1 3 3
1 4 2
4 3 5
2 4 6
3 2 7
```

```
1100
1000
```