#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < (n);i++)
#define sz(x) int(x.size())
typedef long long ll;
typedef pair<int,int> P;
using  Edge = pair<ll,int>;
const ll INF = 1LL<<50;
using Graph = vector<vector<Edge>>;

template<typename T>
vector<vector<T>> dijkstra2(const Graph &G, int s){
  vector<vector<T>> dist(2,vector<T>((int)G.size(),INF));
  priority_queue<pair<Edge,int>, vector<pair<Edge,int>>, greater<pair<Edge,int>> > que;
  dist[0][s] = 0;
  que.push(make_pair(Edge(0,s),0));//暫定距離＋頂点＋チケット

  while (!que.empty()){
    pair<Edge,int> e = que.top(); que.pop();
    int v = e.first.second;
    int use = e.second;
    if (dist[use][v] < e.first.first) continue;
    for (auto p : G[v]) {
      if (dist[use][p.first] > dist[use][v] + p.second) {
        dist[use][p.first] = dist[use][v] + p.second;
        que.push(make_pair(Edge(dist[use][p.first],p.first),use));
      }
      if (!use) {
        if (dist[1][p.first] < e.first.first) continue;
        dist[1][p.first] = e.first.first;
        que.push(make_pair(Edge(dist[1][p.first],p.first),1));
      }
    }
  } 
  return dist;
}



int main(){
  int n, m;
  cin >> n >> m;
  Graph G(n);
  rep(i,m) {
    int a, b, c;
    cin >> a >> b >> c;
    a--;b--;
    G[a].push_back({b,c});
    G[b].push_back({a,c});  
  }

  auto dist2 = dijkstra2<ll>(G,0);
  
  rep(i,n) {
    cout << dist2[0][i] + min(dist2[0][i], dist2[1][i]) << endl;
  }
  return 0;
}