import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.function.Function;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main {
    public static void main(String[] args) {
        Scanner stdin = new Scanner(System.in);
        
        String[] first = stdin.nextLine().split(" ");
        int n = Integer.parseInt(first[0]);
        int m = Integer.parseInt(first[1]);
        
        Map<Integer, Map<Integer, Integer>> costs 
            = IntStream.range(0, n).boxed().collect(Collectors.toMap(Function.identity(), unused -> new HashMap<>()));
        
        for (int i = 0; i < m; i++) {
            String[] line = stdin.nextLine().split(" ");
            int a = Integer.parseInt(line[0]) - 1;
            int b = Integer.parseInt(line[1]) - 1;
            int c = Integer.parseInt(line[2]);
            
            costs.get(a).put(b, c);
            costs.get(b).put(a, c);
        }
        
        int[] d1 = new int[n];
        PriorityQueue<Integer> q1 = new PriorityQueue<>(Comparator.comparing(i -> d1[i]));
        
        Arrays.fill(d1, Integer.MAX_VALUE);
        d1[0] = 0;
        q1.add(0);
        
        while (!q1.isEmpty()) {
            int u = q1.poll();
            for (Entry<Integer, Integer> e : costs.get(u).entrySet()) {
                int v = e.getKey();
                if (d1[u] + e.getValue() < d1[v]) {
                    d1[v] = d1[u] + e.getValue();
                    q1.add(v);
                }
            }
        }
        
        
        int[] d2 = new int[n * 2];
        PriorityQueue<Integer> q2 = new PriorityQueue<>(Comparator.comparing(i -> d2[i]));
        
        Arrays.fill(d2, Integer.MAX_VALUE);
        d2[n * 0 + 0] = 0;
        d2[n * 1 + 0] = 0;
        q2.add(n * 0 + 0);
        q2.add(n * 1 + 0);
        
        while (!q2.isEmpty()) {
            int u = q2.poll();
            int x = u % n;
            boolean skipped = (u / n == 1);
            if (skipped) {
                for (Entry<Integer, Integer> e : costs.get(x).entrySet()) {
                    int y = e.getKey();
                    int v = n * 1 + y;
                    if (d2[u] + e.getValue() < d2[v]) {
                        d2[v] = d2[u] + e.getValue();
                        q2.add(v);
                    }
                }
            } else {
                for (Entry<Integer, Integer> e : costs.get(x).entrySet()) {
                    int y1 = e.getKey();
                    int v1 = n * 0 + y1;
                    if (d2[u] + e.getValue() < d2[v1]) {
                        d2[v1] = d2[u] + e.getValue();
                        q2.add(v1);
                    }
                    
                    int y2 = e.getKey();
                    int v2 = n * 1 + y2;
                    if (d2[u] < d2[v2]) {
                        d2[v2] = d2[u];
                        q2.add(v2);
                    }
                }
            }
        }
        
        for (int i = 0; i < n; i++) {
            System.out.println(d1[i] + d2[n * 1 + i]);
        }
    }
}