- Time limit: 1.00 s
- Memory limit: 512 MB
The first input line has two integers $n$ and $m$: the number of cities and flight connections. The cities are numbered $1,2,\ldots,n$. City 1 is Syrjälä, and city $n$ is Metsälä.
After this there are $m$ lines describing the flights. Each line has three integers $a$, $b$, and $c$: a flight begins at city $a$, ends at city $b$, and its price is $c$. Each flight is unidirectional.
You can assume that it is always possible to get from Syrjälä to Metsälä.
Print one integer: the price of the cheapest route from Syrjälä to Metsälä.
When you use the discount coupon for a flight whose price is $x$, its price becomes $\lfloor x/2 \rfloor$ (it is rounded down to an integer).
- $2 \le n \le 10^5$
- $1 \le m \le 2 \cdot 10^5$
- $1 \le a,b \le n$
- $1 \le c \le 10^9$
1 2 3
2 3 1
1 3 7
2 1 5