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CSES Problem Set

Graph Paths II


Task | Statistics


CSES - Graph Paths IICSES - 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
Example

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


Output:
27