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)

//include
//------------------------------------------
#include <vector>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>
#include <fstream>
using namespace std;

//conversion
//------------------------------------------
inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}

//math
//-------------------------------------------
template<class T> inline T sqr(T x) {return x*x;}

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef pair<long, long> PLL;
typedef long long LL;
//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

//repetition
//------------------------------------------
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

//constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI  = acos(-1.0);

//clear memory
#define CLR(a) memset((a), 0 ,sizeof(a))
#define INF 10000000
#define MAX_V 100000

struct edge{long to,cost;};
typedef pair<LL,long> P;//firstは最短距離,secondは頂点番号

long V;
vector<edge> G[MAX_V];
LL d[MAX_V];

void dijkstra(long s){
	priority_queue<P,vector<P>,greater<P> > que;
	fill(d,d+V,INF);
	d[s]=0;
	que.push(P(0,s));
	
	while(!que.empty()){
		P p=que.top();que.pop();//仮の最短距離が短い順に取り出す
		long v=p.second;
		if(d[v]<p.first)continue;
		REP(i,G[v].size()){
			edge e=G[v][i];
			if(d[e.to]>d[v]+e.cost){
				d[e.to]=d[v]+e.cost;
				que.push(P(d[e.to],e.to));//仮の最短距離と頂点の組を更新が行われる度に追加していく
			}
		}
	}
}

int main(){
	long E,r;
	cin>>V>>E>>r;
	REP(i,E){
		edge e;long f;
		cin>>f>>e.to>>e.cost;
		G[f].PB(e);
	}
	dijkstra(r);
	REP(i,V){
		if(d[i]<INF)cout<<d[i]<<endl;
		else cout<<"INF"<<endl;
	}
	return 0;
}