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CSES Problem Set

# Shortest Routes I

CSES - Shortest Routes ICSES - Shortest Routes I

 Time limit: 1.00 s Memory limit: 512 MB

There are $n$ cities and $m$ flight connections between them. Your task is to determine the length of the shortest route from Syrjälä to every city.

Input

The first input line has two integers $n$ and $m$: the number of cities and flight connections. The cities are numbered $1,2,\dots,n$, and city $1$ is Syrjälä.

After that, there are $m$ lines describing the flight connections. 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 a one-way flight.

You can assume that it is possible to travel from Syrjälä to all other cities.

Output

Print $n$ integers: the shortest route lengths from Syrjälä to cities $1,2,\dots,n$.

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

Input:
3 4 1 2 6 1 3 2 3 2 3 1 3 4

Output:
0 5 2