Steiner tree in random graph

You are given a weighted graph on $n$ vertices. You should find a connected subgraph of minimal weight, which contains all vet rices with numbers from $1$ to $n - k$.

To make problem easier to solve, and tests easier to generate, all tests are generated using following algorithm:

• Integers $n$, $m$, $k$ are chosen.
• All $\frac{n\cdot(n-1)}{2}$ possible edges are shuffled in random order
• Next edge is added to graph if after it is add, it's possible to add some more edges to make graph connected with $m$ edges total.
• For each edge weight is generated uniformly on segment $\[50, 100]$ independent from other edges.

In first line there are three integers $n$ ($5 \le n \le 100$), $m$ ($2\cdot n \le m \le 10\cdot n$), $k$ ($0 \le k \le 30$). On next $m$ lines there are triples of integers $a\_i b\_i w\_i$ ($1 \le a\_i < b\_i \le n$, $50 \le w\_i \le 100$), each of them means, that vertices $a\_i$ и $b\_i$ are connected by edge of weight $w\_i$.

It's guaranteed, that graph have no loops, multiple edges, and in all tests, except samples it's generated by algorithm described above.

In first line, print one integer $c$ --- number of edges in chosen subgraph. In next $c$ lines print chosen edges.