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# (judge verdict: Wrong Answer)

#pragma warning disable

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Numerics;
using System.Collections;
using System.Timers;

static class MainClass
{
    public static void Main(string[] args)
    {
        var VEr = Console.ReadLine().SplittedStringToInt32List();
        var v = VEr[0];
        var e = VEr[1];
        var r = VEr[2];
        var ls = new List<Edge>();
        for (int i = 0; i < e; i++)
        {
            var item = Console.ReadLine().SplittedStringToInt32List();
            var edge = new Edge() { Cost = item[2], From = item[0], To = item[1] };
            ls.Add(edge);
        }
        InitializeBellmanFord(v, e, ls);
        SearchShortestPath(r);
        for (int i = 0; i < v; i++)
        {
            var omomi = ShortestDistances[i];
            if (omomi == INF)
                Console.WriteLine("INF");
            else
                Console.WriteLine(omomi);
        }

        Console.ReadLine();
    }


    // s番目の頂点から各々の頂点への最短距離を求めるBellman-Ford

    public static void InitializeBellmanFord(int v,int e, IEnumerable<Edge> edges)
    {
        V = v;
        Edges = edges.ToArray();
        ShortestDistances = new int[V];
        E = e;
    }

    public class Edge
    {
        public int From;
        public int To;
        public int Cost;
    }

    public static Edge[] Edges;

    public static int[] ShortestDistances;

    public static int V;

    public static int E;

    public static void SearchShortestPath(int s)
    {
        for (int i = 0; i < V; i++)
        {
            ShortestDistances[i] = INF;
        }
        ShortestDistances[s] = 0;
        while (true)
        {
            var update = false;
            for (int i = 0; i < E; i++)
            {
                var e = Edges[i];
                if (ShortestDistances[e.From] != INF && ShortestDistances[e.To] > ShortestDistances[e.From] + e.Cost)
                {
                    ShortestDistances[e.To] = ShortestDistances[e.From] + e.Cost;
                    update = true;
                }
            }
            if (!update)
                break;
        }
    }


    #region ライブラリ
    public static long ToInt64(this string str) => long.Parse(str);
    public static int ToInt32(this string str) => int.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static List<string> SplittedStringToList(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).ToList();
    public static List<int> SplittedStringToInt32List(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => int.Parse(x)).ToList();
    public static List<BigInteger> SplittedStringToBigInteger(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => BigInteger.Parse(x)).ToList();

    public const int INF = int.MaxValue / 4;
    #endregion
}