#include "bits/stdc++.h"
using namespace std;

using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;
using vl = vector<ll>;
ld EPS = 1e-12;
int INF = numeric_limits<int>::max() / 2;
int MOD = 1e9 + 7;
#define rep(i,n) for(int i = 0; i < n; i++)
#define all(obj) (obj).begin(), (obj).end()
#define debug(x) cerr << #x << ": " << x << '\n'

vector<vector<int> > edge(100010, vector<int>(0)); //頂点iのj番目の辺の行き先
vector<vector<int> > dist(100010, vector<int>(0)); //頂点iのj番目の辺の重み
vector<int> longest(100010,0);

vector<int> d(100010,-1);
vector<int> dn(100010,-1);

int dijkstra_prime(int from, int to, int v){
    for(int i = 0; i < v; i++){
        dn[i] = INF;
    }
    dn[from] = 0;
    priority_queue<int> q;
    q.push(from);

    while(!q.empty()){
        int now = q.top();
        q.pop();
        //その頂点からたどり着ける頂点の情報を更新する
        for(int j = 0; j < edge[now].size(); j++){
            int next = edge[now][j];
            int nextd = dn[now] + longest[now] + dist[now][j];
            int nextlong = max(longest[now], dist[now][j]);
            if(nextd - nextlong < dn[next]){
                dn[next] = nextd - nextlong;
                longest[next] = nextlong;
                q.push(next);
            }
        }
    }

    return dn[to];
}

int dijkstra(int from, int to, int v){
    for(int i = 0; i < v; i++){
        d[i] = INF;
    }
    d[from] = 0;
    priority_queue<int> q;
    q.push(from);

    while(!q.empty()){
        int now = q.top();
        q.pop();
        //その頂点からたどり着ける頂点の情報を更新する
        for(int j = 0; j < edge[now].size(); j++){
            int next = edge[now][j];
            int nextd = d[now] + dist[now][j];
            if(nextd < d[next]){
                d[next] = nextd;
                q.push(next);
            }
        }
    }

    return d[to];
}
 
int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n,m;
    cin >> n >> m;
    rep(i,m){
        int a,b,c;
        cin >> a >> b >> c;
        a--;b--;
        edge[a].push_back(b);
        dist[a].push_back(c);
        edge[b].push_back(a);
        dist[b].push_back(c);
    }
    dijkstra(0,0,n);
    dijkstra_prime(0,0,n);
    rep(i,n){
        cout << d[i] + dn[i] << '\n';
    }
    
    return 0;
}