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: Wrong Answer)

object Main {

  def main(args: Array[String]): Unit = {
    import scala.collection.mutable.ListBuffer
    import scala.collection.mutable.ArrayBuffer
    val sc = new java.util.Scanner(System.in)

    val INF = Int.MaxValue / 2 - 1
    val Vs, Es, r = sc.nextInt()
    val E = Array.fill(Vs)(ArrayBuffer[(Int, Int)]())
    (0 until Es) foreach { _ =>
      val u, v, w = sc.nextInt()
      E(u).append((v, w))
    }
    val W = Array.fill(Vs)(INF)

    def topologicalSort(E: Array[ArrayBuffer[(Int, Int)]]): Seq[Int] = {
      val sortedV = new ListBuffer[Int]()
      val visited = new Array[Boolean](Vs)
      def recursive(u: Int): Unit = {
        E(u) foreach { case (v, _) =>
          if (!visited(v)) {
            visited(v) = true
            recursive(v)
          }
        }
        sortedV.prepend(u)
      }
      (0 until Vs) foreach recursive
      sortedV
    }

    topologicalSort(E) foreach { u =>
      E(u) foreach { case (v, w) =>
        if (W(v) > W(u) + w)
          W(v) = W(u) + w
      }
    }
  }

}