import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner stdin = new Scanner(System.in);
        int n = Integer.parseInt(stdin.next());
        int m = Integer.parseInt(stdin.next());
        
        Map<Integer, Map<Integer, Integer>> costs = new HashMap<>();
        for (int i = 0; i < m; i++) {
            int a = Integer.parseInt(stdin.next()) - 1;
            int b = Integer.parseInt(stdin.next()) - 1;
            int c = Integer.parseInt(stdin.next());
            
            costs.computeIfAbsent(a, unused -> new HashMap<>()).put(b, c);
            costs.computeIfAbsent(b, unused -> new HashMap<>()).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 (int v : costs.getOrDefault(u, Collections.emptyMap()).keySet()) {
                if (d1[u] + costs.get(u).get(v) < d1[v]) {
                    d1[v] = d1[u] + costs.get(u).get(v);
                    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 (int y : costs.getOrDefault(x, Collections.emptyMap()).keySet()) {
                    int v = n * 1 + y;
                    if (d2[u] + costs.get(x).get(y) < d2[v]) {
                        d2[v] = d2[u] + costs.get(x).get(y);
                        q2.add(v);
                    }
                }
            } else {
                for (int y : costs.getOrDefault(x, Collections.emptyMap()).keySet()) {
                    int v = n * 0 + y;
                    if (d2[u] + costs.get(x).get(y) < d2[v]) {
                        d2[v] = d2[u] + costs.get(x).get(y);
                        q2.add(v);
                    }
                }
                
                for (int y : costs.getOrDefault(x, Collections.emptyMap()).keySet()) {
                    int v = n * 1 + y;
                    if (d2[u] < d2[v]) {
                        d2[v] = d2[u];
                        q2.add(v);
                    }
                }
            }
        }
        
        for (int i = 0; i < n; i++) {
            System.out.println(d1[i] + d2[n * 1 + i]);
        }
    }
}