There are $n$ cities and $m$ routes through which parcels can be carried from one city to another city. For each route, you know the maximum number of parcels and the cost of a single parcel.
You want to send $k$ parcels from Syrjälä to Lehmälä. What is the cheapest way to do that?
The first input line has three integers $n$ , $m$ and $k$ : the number of cities, routes and parcels. The cities are numbered $1,2,\dots,n$ . City $1$ is Syrjälä and city $n$ is Lehmälä.
After this, there are $m$ lines that describe the routes. Each line has four integers $a$ , $b$ , $r$ and $c$ : there is a route from city $a$ to city $b$ , at most $r$ parcels can be carried through the route, and the cost of each parcel is $c$ .
Print one integer: the minimum total cost or $-1$ if there are no solutions.
4 5 3 1 2 5 100 1 3 10 50 1 4 7 500 2 4 8 350 3 4 2 100· · \n · · · \n · · · \n · · · \n · · · \n · · · \n
750\n
One parcel is delivered through route $1 \rightarrow 2 \rightarrow 4$ (cost $1 \cdot 450=450$ ) and two parcels are delivered through route $1 \rightarrow 3 \rightarrow 4$ (cost $2 \cdot 150=300$ ).