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CSES Problem Set

Flight Routes

CSES - Flight RoutesCSES - Flight Routes

 Time limit: 1.00 s Memory limit: 512 MB

Your task is to find the $k$ shortest flight routes from Syrjälä to Metsälä. A route can visit the same city several times.

Input

The first input line has three integers $n$, $m$, and $k$: the number of cities, the number of flights, and the parameter $k$. The cities are numbered $1,2,\ldots,n$. City 1 is Syrjälä, and city $n$ is Metsälä.

After this, the input has $m$ 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 $c$. All flights are unidirectional.

You may assume that there are at least $k$ distinct routes from Syrjälä to Metsälä.

Output

Print $k$ integers: the prices of the $k$ cheapest routes sorted according to their prices. You can assume that there are at least $k$ different routes.

Constraints
• $2 \le n \le 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le a,b \le n$
• $1 \le c \le 10^9$
• $1 \le k \le 10$
Example

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

Output:
5 7 8