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