use std::{cmp::Reverse, collections::BinaryHeap};

const INF: usize = 1usize << 60;

fn dijkstra(start: usize, paths: &Vec<Vec<(usize, usize)>>) -> Vec<Vec<usize>> {
    let n = paths.len();
    let mut que = BinaryHeap::new();
    que.push((Reverse(0), 0, start));
    let mut costs = vec![vec![INF; 2]; n];
    costs[start][0] = 0;
    costs[start][1] = 0;
    while let Some((Reverse(cost), used, u)) = que.pop() {
        if cost > costs[u][used] { continue; }
        for &(v, vcost) in paths[u].iter() {
            if costs[u][used] + vcost < costs[v][used] {
                costs[v][used] = costs[u][used] + vcost;
                que.push((Reverse(costs[v][used]), used, v));
            }
            if used == 0 && costs[u][0] < costs[v][1] {
                costs[v][1] = costs[u][0];
                que.push((Reverse(costs[v][1]), 1, v));
            }
        }
    }
    costs
}

fn main() {
    let mut nm = String::new();
    std::io::stdin().read_line(&mut nm).ok();
    let nm: Vec<usize> = nm.trim().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let n = nm[0];
    let m = nm[1];
    let mut paths = vec![vec![]; n];
    for _ in 0..m {
        let mut abc = String::new();
        std::io::stdin().read_line(&mut abc).ok();
        let abc: Vec<usize> = abc.trim().split_whitespace().map(|s| s.parse().unwrap()).collect();
        let a = abc[0]-1;
        let b = abc[1]-1;
        let c = abc[2];
        paths[a].push((b, c));
        paths[b].push((a, c));
    }

    let dists = dijkstra(0, &paths);
    for i in 0..n {
        println!("{}", dists[i][0] + dists[i][1]);
    }
}