You are to write a program that receives a weighted directed graph and finds
distances from source vertex S to all other vertices. Distance from S to
some vertex W is the minimal length of path going from S to W.
Length of path is the sum of weights of its edges.

Vertices are numbered with integers from 1 to N.

Input file format

First line of input file contains three integers NM and S,
where M is the number of edges. Next M lines contain three
integers each —
starting vertex number, ending vertex number and weight of some edge respectively.
All weights are positive.
There is at most one edge connecting two vertices in every direction.

Output file format

Output file must contain N integers — distances from
source vertex to all vertices.
If some vertices are not reachable from S, corresponding numbers must be −1.

Constraints

1 ≤ N ≤ 1000.
All weights are less or equal than 1000.