Description

Input

In the first line of input there are three integers $n$, $m$, and $k$ ($2 \leq n \leq 10^{5}$, $1 \leq m \leq 10^{5}$, $1 \leq k \leq 20$) — the number of cities, the number of roads, and the maximal number of flights Stanley can take.

The following $m$ lines describe the roads. Each contains three integers $u$, $v$, $w$ ($1 \leq u, v \leq n$, $u \neq v$, $1 \leq w \leq 10^{9}$) — the cities the road connects and the time it takes to ride through. Note that some pairs of cities may be connected by more than one road.

Output

Print $n$ integers, $i$-th of which is equal to the minimum time of traveling to city $i$.

3 1 2
1 3 1

0 1 1

4 3 1
1 2 3
2 4 5
3 4 7

0 1 4 6

2 1 1
2 1 893746473

0 1

5 5 2
2 1 33
1 5 93
5 3 48
2 3 21
4 2 1

0 1 2 2 3

Note

In the first sample, it takes no time to get to city 1; to get to city 2 it is possible to use a flight between 1 and 2, which will take 1 unit of time; to city 3 you can get via a road from city 1, which will take 1 unit of time.

In the second sample, it also takes no time to get to city 1. To get to city 2 Stanley should use a flight between 1 and 2, which will take 1 unit of time. To get to city 3 Stanley can ride between cities 1 and 2, which will take 3 units of time, and then use a flight between 2 and 3. To get to city 4 Stanley should use a flight between 1 and 2, then take a ride from 2 to 4, which will take 5 units of time.