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 PHP (judge verdict: Wrong Answer)

maxd = 10001
nv, ne, r = [int(n) for n in input().split(' ')]
vertices = {k: {} for k in range(nv)}
for i in range(ne):
    s, t, w = [int(n) for n in input().split(' ')]
    vertices[s][t] = w

q = {v for v in vertices}
dist = {v: maxd for v in vertices}
dist[r] = 0

while len(q):
    min = maxd
    u = nv
    for v in q:
        if dist[v] <= min:
            min = dist[v]
            u = v

    q.remove(u)
    for v in vertices[u]:
        alt = dist[u] + vertices[u][v]
        if alt < dist[v]:
            dist[v] = alt

[print(d) if d < maxd else print("INF") for v, d in dist.items()]