7673: [CSES Problem Set] Graph Paths II
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Description
Consider a directed graph that has $n$ nodes and $m$ edges.
Your task is to count the number of paths from node $1$ to node $n$ with exactly $k$ edges.
Your task is to count the number of paths from node $1$ to node $n$ with exactly $k$ edges.
Input
The first input line contains three integers $n, m, k$: 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 $a,b,c$: there is an edge from node $a$ to node $b$ with weight $c$.
Then, there are $m$ lines describing the edges. Each line contains three integers $a,b,c$: 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
$1≤n≤100$
$1 \le m \le n(n-1)$
$1 \le k \le 10^9$
$1 \le a,b \le n$
$1 \le m \le n(n-1)$
$1 \le k \le 10^9$
$1 \le a,b \le n$
Sample 1 Input
3 4 8
1 2 5
2 3 4
3 1 1
3 2 2
Sample 1 Output
27