#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cassert>
#include <iostream>
#include <iomanip>
#include <string>
#include <stack>
#include <queue>
#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <bitset>

#define all(c) c.begin(), c.end()
#define rall(c) c.rbegin(), c.rend()
#define debug(x) cerr << #x << ": " << x << endl

using namespace std;

typedef long long ll;
typedef pair<ll, ll> Pll;
typedef pair<int, int> Pii;

const ll MOD = 1000000007;
const long double EPS = 1e-10;
const int MAX_N = 112345;
const int dyx[4][2] = {
    { 0, 1}, {-1, 0}, {0,-1}, {1, 0}
};

map<ll, ll> d[2];
vector< vector<Pll> > edges(MAX_N);

struct State {
    ll d, longest_edge;
    int node;
    State(int node, ll d, ll longest_edge): node(node), d(d), longest_edge(longest_edge) {}
    bool operator>(const State& s) const{
        return d+longest_edge > s.d+s.longest_edge;
    }
};

void dijkstra(ll start, int shortcut){
    priority_queue<State, vector<State>, greater<State> > que;

    d[shortcut][start] = 0;
    que.push(State(start, 0, 0));

    while(!que.empty()){
        State v = que.top(); que.pop();
        if(d[shortcut].find(v.node) != d[shortcut].end() && d[shortcut][v.node] < v.d) continue;

        for(Pll e: edges[v.node]){
            if(shortcut) {
                if(d[1].find(e.first) == d[1].end() || d[1][e.first] > d[1][v.node] + v.longest_edge + e.second - max(v.longest_edge, e.second)){
                    d[1][e.first] = d[1][v.node] + v.longest_edge + e.second - max(v.longest_edge, e.second);
                    que.push(State(e.first, d[1][e.first], max(v.longest_edge, e.second)));
                }
            } else {
                if(d[0].find(e.first) == d[0].end() || d[0][e.first] > d[0][v.node] + e.second){
                    d[0][e.first] = d[0][v.node] + e.second;
                    que.push(State(e.first, d[0][e.first], 0));
                }
            }
            
        }
    }
}

int main() {
    std::ios::sync_with_stdio(0); cin.tie(0);
    int n,m,a,b; ll c;
    cin >> n >> m;
    for(int i=0;i<m;++i) {
        cin >> a >> b >> c;
        edges[a].emplace_back(b, c);
        edges[b].emplace_back(a, c);
    }

    dijkstra(1LL, 0);
    dijkstra(1LL, 1);

    for(int i=1;i<=n;++i) {
        cout << d[0][i] + d[1][i] << endl;
        // cerr << i << ": " << d[0][i] << " "  << d[1][i] << " " << longest_edge[i] << endl;
    }
}