Problem J. Ford-Bellman ≡

Author:	StdAlg		Time limit:	1 sec
Input file:	input.txt		Memory limit:	8 Mb
Output file:	output.txt

Statement

You are to write a program that finds shortest distances from vertex S to all other vertices in a given directed weighted graph. Graph consists of N vertices, numbered from 1 to N, and M edges.

Input file format

Input file contains two integers N M S, followed my M triplets of integers u_i v_i w_i — starting vertex, ending vertex and weight or the edge. There is at most one edge connecting any two vertices in every direction. There are no cycles of negative weight.

Output file format

Output file must contain a vector of N integers — distances from vertex S to other vertices. The distance from any vertex to itself is considered to be 0. If some vertex is not reachable from S, corresponding cell of the vector must contain empty space.

Constraints

0 ≤ N, M ≤ 1000. All weights are less than 1000 by absolute value.

Sample tests

No.	Input file (input.txt)	Output file (output.txt)
1	3 3 1 1 2 5 1 3 10 2 3 2	0 5 7

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