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: Runtime Error)

object Main {

  def main(args: Array[String]): Unit = {
    val sc = new java.util.Scanner(System.in)

    val INF = Int.MaxValue / 2

    val Vs, Es, root = sc.nextInt()
    val E = (0 until Es) map { _ =>
      val s, t, d = sc.nextInt()
      (s, t, d)
    }
    val W = Array.fill(Vs)(INF)
    W(root) = 0
    // ベルマンフォード, |V|-1回, 全ての辺を緩和させる
    (0 until Vs - 1) foreach { _ =>
      E foreach { case (u, v, w) =>
        if (W(v) > W(u) + w) {
          W(v) = W(u) + w
        }
      }
    }

    println(W. take(Vs). map { w =>
      if (w == INF) "INF" else w.toString
    }. mkString("\n"))
  }

}