CSES - Graph Paths II
• 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.

Input

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 $c$.

Output

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

Constraints
• $1 \le n \le 100$
• $1 \le m \le n(n-1)$
• $1 \le k \le 10^9$
• $1 \le a,b \le n$
• $1 \le c \le 10^9$
Example

Input:
3 4 8 1 2 5 2 3 4 3 1 1 3 2 2

Output:
27