Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in Scala (judge verdict: Time Limit Exceeded)

object Main {
    def main(args: Array[String]) = {
        val inf = Int.MaxValue-10000
        val in = io.Source.stdin.getLines.map(_.split(" ").map(_.toInt)).toList
        val Array(v, _, r) = in.head
        val scanEdges = (g: Array[Int]) => in.tail.foldLeft(g)((a, b) => {
            if (a(b(0)) + b(2) < a(b(1))) a.updated(b(1), a(b(0)) + b(2))
            else a
        })
        def last(l: Stream[Array[Int]]): Array[Int] = {
            if (l.head sameElements l.tail.head) l.head
            else last(l.tail)
        }
        last(Stream.continually(scanEdges).scanLeft(Array.fill(v)(inf).updated(r, 0))((arr, f) => f(arr)))
            .foreach(n => if (n == inf) println("INF") else println(n))
    }
}