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: Time Limit Exceeded)

Infinity = 2 << 33

def getMin q
  min = Infinity
  u = -1
  target = -1
  q.size().times do |i|
    if q[i][1] < min
      min = q[i][1]
      u = q[i][0]
      target = i
    end
  end
  q.delete_at target
  u
end

def dijkstra graph, s
  n = graph.size
  dist = Array.new(n, Infinity)
  dist[s] = 0
  q = Array.new
  q << [s, dist[s]]

  until q.empty?
    u = getMin q
    graph[u].each do |edge|
      v = edge[0]
      w = edge[1]
      total = dist[u] + w
      if total < dist[v]
        dist[v] = total
        q << [v, dist[v]]
      end
    end
  end

  dist
end

v,e,r = $stdin.gets.chomp.split(" ").map(&:to_i)
graph = Array.new(v).map{Array.new}
e.times do
  s,t,d = $stdin.gets.chomp.split(" ").map(&:to_i)
  graph[s] << [t, d]
end
dist = dijkstra(graph, r)
dist.each do |cost|
  puts((cost == Infinity)? "INF" : cost)
end