Shortest Path - Single Source Shortest Path

Time Limit : 3 sec, Memory Limit : 131072 KB
Japanese version is here

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

```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

```4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5
```

```0
1
3
4
```

```4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5
```

```3
0
2
INF
```