import java.io.*;
import java.util.*;
import java.util.stream.*;

public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner();
        int n = sc.nextInt();
        int m = sc.nextInt();
        ArrayList<ArrayList<Path>> graph = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            graph.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            int c = sc.nextInt();
            graph.get(a).add(new Path(b, c));
            graph.get(b).add(new Path(a, c));
        }
        PriorityQueue<Path> queue = new PriorityQueue<>();
        queue.add(new Path(0, 1, 0));
        queue.add(new Path(0, 0, 0));
        long[][] costs = new long[2][n];
        for (long[] arr : costs) {
            Arrays.fill(arr, Long.MAX_VALUE);
        }
        while (queue.size() > 0) {
            Path p = queue.poll();
            if (costs[p.type][p.idx] <= p.value) {
                continue;
            }
            costs[p.type][p.idx] = p.value;
            for (Path x : graph.get(p.idx)) {
                queue.add(new Path(x.idx, p.type, x.value + p.value));
                if (p.type == 0) {
                    queue.add(new Path(x.idx, 1, p.value));
                }
            }
        }
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < n; i++) {
            sb.append(costs[0][i] + costs[1][i]).append("\n");
        }
        System.out.print(sb);
    }
    
    static class Path implements Comparable<Path> {
        int idx;
        int type;
        long value;
        
        public Path(int idx, int type, long value) {
            this.idx = idx;
            this.type = type;
            this.value = value;
        }
        
        public Path(int idx, long value) {
            this(idx, 0, value);
        }
        
        public int compareTo(Path another) {
            if (value == another.value) {
                return 0;
            } else if (value < another.value) {
                return -1;
            } else {
                return 1;
            }
        }
    }
}
class Utilities {
    static String arrayToLineString(Object[] arr) {
        return Arrays.stream(arr).map(x -> x.toString()).collect(Collectors.joining("\n"));
    }
    
    static String arrayToLineString(int[] arr) {
        return String.join("\n", Arrays.stream(arr).mapToObj(String::valueOf).toArray(String[]::new));
    }
}
class Scanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    StringBuilder sb = new StringBuilder();
    
    public Scanner() throws Exception {
        
    }
    
    public int nextInt() throws Exception {
        return Integer.parseInt(next());
    }
    
    public long nextLong() throws Exception {
        return Long.parseLong(next());
    }
    
    public double nextDouble() throws Exception {
        return Double.parseDouble(next());
    }
    
    public int[] nextIntArray() throws Exception {
        return Stream.of(br.readLine().split(" ")).mapToInt(Integer::parseInt).toArray();
    }
    
    public String next() throws Exception {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }
    
}