Problem: 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).

Constraints

* 1 ≤ |V| ≤ 100000
* 0 ≤ di ≤ 10000
* 0 ≤ |E| ≤ 500000
* There are no parallel edges
* There are no self-loops

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.

Examples

Input

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


Output

0
1
3
4


Input

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


Output

3
0
2
INF

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;

class Pair<E extends Comparable<E>,F extends Comparable<F>> implements Comparable<Pair<E,F>>{
    E first;
    F second;
    public Pair(E first, F second){
        this.first=first;
        this.second=second;
    }
    public E getFirst(){return first;}
    public F getSecond(){return second;}
    public String toString(){
        return "<"+first.toString()+","+second.toString()+">";
    }
    public int hashCode(){
        return first.hashCode()*30011+second.hashCode()+2;
    }
    public boolean equals(Object obj) {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;
        Pair another = (Pair) obj;
        return this.getFirst().equals(another.getFirst())&&this.getSecond().equals(another.getSecond());
    }

    public int compareTo(Pair<E,F> another){
        if(this.getFirst().equals(another.getFirst())){
            return this.getSecond().compareTo(another.getSecond());
        }
        return this.getFirst().compareTo(another.getFirst());
    }

}

class Graph{
    private static final Long INF = 5000000000000000L;
    static class InfiniteAnswerException extends Exception{
        public InfiniteAnswerException(){
            super();
        }
        public InfiniteAnswerException(String msg){
            super(msg);
        }
    }
    static class NoPathExistException extends Exception{
        public NoPathExistException(){
            super();
        }
        public NoPathExistException(String msg){
            super(msg);
        }
    }

    int nodeNum;
    Map<Integer, Long>[] connectedNode;

    @SuppressWarnings("unchecked")
    public Graph(int N){
        nodeNum = N;
        connectedNode = new Map[nodeNum]; // !!!
        for(int n=0; n<N; n++) connectedNode[n] = new HashMap<>();
    }
    void addDirectionalEdge(int from, int to, long weight){
        connectedNode[from].put(to, weight);
    }
    void addEdge(int u, int v, long weight){
        addDirectionalEdge(u, v, weight);
        addDirectionalEdge(v, u, weight);
    }
    long edgeDistance(int from, int to){
        return connectedNode[from].getOrDefault(to, INF);
    }
    long pathDistance(int[] path){
        long ans = 0;
        for(int i=0; i<path.length-1; i++){
            ans += edgeDistance(path[i], path[i+1]);
        }
        return ans;
    }
    
    long pathDistance(Integer[] path){
        long ans = 0;
        for(int i=0; i<path.length-1; i++){
            ans += edgeDistance(path[i], path[i+1]);
        }
        return ans;
    }
    
    long pathDistance(List<Integer> path){
        return pathDistance(path.toArray(new Integer[path.size()]));
    }
    
    Graph copy(){
        Graph G = new Graph(this.nodeNum);
        for(int from=0; from<nodeNum; from++) for(int to:connectedNode[from].keySet()){
            G.addDirectionalEdge(from, to, this.edgeDistance(from,to));
        }
        return G;
    }

    long[] dijkstra(int start){
        long[] distance = new long[nodeNum];
        Arrays.fill(distance, INF);
        distance[start] = 0;
        int[] prev = new int[nodeNum];
        Arrays.fill(prev, -1);

        PriorityQueue<Pair<Long,Integer>> Q = new PriorityQueue<Pair<Long,Integer>>();
        Q.add(new Pair<>(distance[start], start));

        while(!Q.isEmpty()){
            Pair<Long,Integer> pair = Q.poll();
            int u = pair.second;
            for(int v: connectedNode[u].keySet()){
                long nextDistance = distance[u] + edgeDistance(u,v);
                if(nextDistance < distance[v]){
                    distance[v] = nextDistance;
                    prev[v] = u;
                    Q.add(new Pair<>(distance[v], v));
                }
            }
        }
        return distance;
    }
    List<Integer> dijkstraPath(int start, int end) throws NoPathExistException {
        long[] distance = new long[nodeNum];
        Arrays.fill(distance, INF);
        distance[start] = 0;
        int[] prev = new int[nodeNum];
        Arrays.fill(prev, -1);

        PriorityQueue<Pair<Long,Integer>> Q = new PriorityQueue<Pair<Long,Integer>>();
        Q.add(new Pair<>(distance[start], start));

        while(!Q.isEmpty()){
            Pair<Long,Integer> pair = Q.poll();
            int u = pair.second;
            for(int v: connectedNode[u].keySet()){
                long nextDistance = distance[u] + edgeDistance(u,v);
                if(nextDistance < distance[v]){
                    distance[v] = nextDistance;
                    prev[v] = u;
                    Q.add(new Pair<>(distance[v], v));
                }
            }
        }

        LinkedList<Integer> ans = new LinkedList<>();
        ans.push(end);
        int cur = end;
        while(cur!=start){
            if(cur==-1) throw new NoPathExistException("No path exist: "+start+" to "+end);
            ans.push(prev[cur]);
            cur = prev[cur];
        }
        return ans;
    }

    long[] bellmanford(int start) throws InfiniteAnswerException{
        //time order: O(nodeNum * edgeNum)
        long[] distance = new long[nodeNum];
        Arrays.fill(distance, INF);
        distance[start] = 0;

        for(int time=0; time<nodeNum-1; time++){
            for(int from=0; from<nodeNum; from++) for(int to: connectedNode[from].keySet()){
                long w = this.edgeDistance(from, to);
                if(distance[to] > distance[from] + w) distance[to] = distance[from] + w;
            }
        }
        for(int from=0; from<nodeNum; from++) for(int to: connectedNode[from].keySet()){
            long w = this.edgeDistance(from, to);
            if(distance[to] > distance[from] + w){
                throw new InfiniteAnswerException("this graph has negative cycles[BF-alg]");
            }
        }
        return distance;
    }
}

class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int V = sc.nextInt();
        int E = sc.nextInt();
        int root = sc.nextInt();

        Graph G = new Graph(V);
        for(int e=0; e<E; e++){
            int s = sc.nextInt();
            int t = sc.nextInt();
            long d = sc.nextLong();
            G.addDirectionalEdge(s, t, d);
        }

        long[] distance = G.dijkstra(root);
        for(int v=0; v<V; v++){
            System.out.println(distance[v]<5_000_000_000_000_000L ? distance[v] : "INF");
        }

    }
}