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**Task** | Statistics

Time limit: | 1.00 s | Memory limit: | 512 MB |

Consider a directed weighted graph having $n$ nodes and $m$ edges. Your task is to calculate the minimum path length from node $1$ to node $n$ with exactly $k$ edges.

The first input line contains three integers $n$, $m$ and $k$: the number of nodes and edges, and the length of the path. The nodes are numbered $1,2,\dots,n$.

Then, there are m lines describing the edges. Each line contains three integers $a$, $b$ and $c$: there is an edge from node $a$ to node $b$ with weight $c$.

Print the minimum path length. If there are no such paths, print $-1$.

- $1 \le n \le 100$

- $1 \le m \le n(n-1)$

- $1 \le k \le 10^9$

- $1 \le a,b \le n$

- $1 \le c \le 10^9$

Input:

`3 4 8`

1 2 5

2 3 4

3 1 1

3 2 2

Output:

`27`