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: Memory Limit Exceeded)

class SimpleDirectedGraph
  def initialize(v = 0)
    @g = v.times.map{ [Float::INFINITY] * v }
  end
  
  def add_edge(v1, v2, w)
    @g[v1][v2] = w
    return @g
  end
  
  def dijkstra(r)
    # initialize
    v_num = @g.length
    dist, visited = [Float::INFINITY] * v_num, [false] * v_num
    dist[r] = 0
    
    loop do
      v = nil
      
      v_num.times do |u|
        v = u if(!visited[u] && (!v || dist[u] < dist[v]))
      end
    
      break unless v
      
      visited[v] = true
      
      v_num.times do |u|
        dist[u] = [dist[u], dist[v] + @g[v][u]].min
      end
    end
    
    return dist
  end
end

v, e, r = gets.split.map(&:to_i)
graph = SimpleDirectedGraph.new(v)

e.times do
  s, t, d = gets.split.map(&:to_i)
  graph.add_edge(s, t, d)
end

graph.dijkstra(r).each do |i|
  puts i == Float::INFINITY ? "INF" : i
end