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 Ruby (judge verdict: Accepted)

class Edge
  attr_accessor :s, :t, :d
  def initialize(arr)
    self.s = arr[0]
    self.t = arr[1]
    self.d = arr[2]
  end
end

v, e, r = gets.strip.split(' ').map(&:to_i)

es = []

e.times do
  edge = Edge.new(gets.strip.split(' ').map(&:to_i))
  es << edge
end

d = Array.new(v, Float::INFINITY)
d[r] = 0;

loop do
  update = false
  e.times do |i|
    edge = es[i]
    if d[edge.s] == Float::INFINITY
      next
    end
    dd = d[edge.s] + edge.d
    if d[edge.t] > dd
      d[edge.t] = dd
      update = true
    end
  end

  break unless update
end

d.each do |i|
  if i == Float::INFINITY
    puts "INF"
  else
    puts i
  end
end