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 C++11 (judge verdict: Accepted)

// SingleSourceShortestPath by Bellman - Ford
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_A&lang=jp
//
//

#include<iostream>

using namespace std;

#define EDGES 500000
#define VERTICES 100000


int V, E, r, S[EDGES+10], T[EDGES+10], D[EDGES+10];
const int INF = 10000*100000+100;
int C[VERTICES + 1];

void solve();

int main(){
    cin >> V >> E >> r;

    for(int i = 0; i < E; ++i){
        cin >> S[i] >> T[i] >> D[i];
    }

    solve();
}

void solve(){
    for(int i = 0; i < V; ++i){//距離リストの初期化
        C[i] = INF;
    }

    C[r] = 0;

    for(int i = 1; i < V; ++i){
        bool update = false;
        for(int j = 0; j < E; ++j){
            int u = S[j], v = T[j];
            if(C[v] > (C[u] + D[j])) {
                C[v] = C[u] + D[j];
                update = true;
            }
        }
        if (!update) break; //一巡して更新が無くなるまで続ける
    }

    for(int i = 0; i < V; ++i){//距離リストの出力
        if(C[i] == INF) 
            cout << "INF" << endl;
        else
            cout << C[i] << endl;
    }
}