#include <bits/stdc++.h>
#include <unordered_set>
using namespace std;
#define ll long long
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define repeat(i,s,n) for(int (i)=s; (i)<(n); (i)++)
#define revrep(i,n) for(int (i)=(n)-1;i>=0; i--)

// example const ll inf=1e15;
void dijkstra(int s, map<int,map<int,ll>>& g, vector<vector<ll>>& dist,const ll inf, const ll zero) {
  int n=dist[0].size();
  vector<vector<bool>> visited = vector<vector<bool>>(2, vector<bool>(n));
  fill(dist[0].begin(),dist[0].end(),inf);
  fill(dist[1].begin(),dist[1].end(),inf);
  using P = tuple<ll,int,int>;
  priority_queue<P,vector<P>, greater<P>> pq;
  dist[0][s]=zero;
  dist[1][s]=zero;
  //visited[s]=true;
  pq.push(make_tuple(0,s,0));
  pq.push(make_tuple(0,s,1));
  while(!pq.empty()) {
    int v,b;
    ll d;
    tie(d,v,b)=pq.top();
    pq.pop();
    if(visited[b][v]) continue;
    visited[b][v]=true;
    for(auto& uw : g[v]) {
      int u;
      ll w;
      tie(u,w)=uw;
      if(b==0) {
        if(visited[0][u])continue;
        if(d<dist[1][u]) {
          dist[1][u]=d;
          pq.push(make_tuple(dist[1][u],u,1));
        }
        if(d+w<dist[0][u]) {
          dist[0][u]=d+w;
          pq.push(make_tuple(dist[0][u],u,0));
        }
      } else {
        // b=1
        if(visited[1][u]) continue;
        if(d+w<dist[1][u]) {
          dist[1][u]=d+w;
          pq.push(make_tuple(dist[1][u],u,1));
        }
      }
    }
  }
}

void dfs(int s, vector<ll>& min_c, vector<vector<int>>& ng,map<int,map<int,ll>>& g) {
  // we have min_c[s]
  for(auto& u : ng[s]) {
    min_c[u]=min(min_c[s],g[s][u]);
    dfs(u,min_c,ng,g);
  }
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout<<setprecision(std::numeric_limits<float>::max_digits10);
  int n,m;
  cin>>n>>m;
  map<int,map<int,ll>> g;
  rep(i,m) {
    ll a,b,c;
    cin>>a>>b>>c;
    g[a-1][b-1]=c;
    g[b-1][a-1]=c;
  }
  vector<vector<ll>> dist = vector<vector<ll>>(2,vector<ll>(n));
  const ll inf=1e15;
  dijkstra(0,g,dist,inf,0LL);
  rep(i,n) {
    cout << dist[0][i]+dist[1][i]<<endl;
  }
  return 0;
}