#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pll;
typedef tuple<ll,ll,ll> tl;
ll inf=1000000000000000000;
struct edge{ll len,ma,num;};
bool cmp(edge a,edge b){
  if(a.len!=b.len)return a.len<b.len;
  else{
    if(a.ma!=b.ma)return a.ma<b.ma;
    else{
      if(a.num!=b.num)return a.num<b.num;
      return true;
    }
  }
}
int main(){
    ll n,m;cin>>n>>m;
    vector<pll> v[n+1];
    for(ll i=0;i<m;i++){
        ll a,b,c;cin>>a>>b>>c;
        v[a].push_back(make_pair(b,c));
        v[b].push_back(make_pair(a,c));
    }
    ll d[n+1],da[n+1];
    fill(d,d+n+1,inf);
    fill(da,da+n+1,inf);
    priority_queue<pll,vector<pll>,greater<pll>> q;
    q.push(make_pair(0,1));
    bool used[n+1];
    fill(used,used+n+1,false);
    d[1]=0;
    while(q.size()>0){
        pll p=q.top();q.pop();
        ll pf=p.first,ps=p.second;
        if(used[ps])continue;
        used[ps]=true;
        for(ll i=0;i<v[ps].size();i++){
            ll now=v[ps][i].first;
            ll dis=v[ps][i].second;
            if(used[now])continue;
            if(d[now]>dis+pf){
                d[now]=dis+pf;
                q.push(make_pair(dis+pf,now));
            }
        }
        
    }
  
    fill(used,used+n+1,false);
    
    priority_queue<tl,vector<tl>,greater<tl>> qq;
    qq.push(make_tuple(0,0,1));
    da[1]=0;
    while(qq.size()>0){
        tl t=qq.top();qq.pop();
        ll tf=get<0>(t),ts=get<1>(t),tt=get<2>(t);
        if(used[tt])continue;
        used[tt]=true;
      //cout<<tf<<" "<<ts<<" "<<tt<<endl;
        for(int i=0;i<v[tt].size();i++){
            ll now=v[tt][i].first;
            ll dis=v[tt][i].second;
            ll u=dis+tf;
          ll y=ts;
          if(used[now])continue;
            if(ts<dis){
                u-=dis-ts;
                y=dis;
            }
            if(da[now]>u){
                da[now]=u;
                qq.push(make_tuple(u,y,now));
            }
        }
    }
    for(ll i=1;i<=n;i++)cout<<d[i]+da[i]<<endl;
  for(ll i=1;i<=n;i++){
    //cout<<d[i]<<" "<<da[i]<<endl;
  }
}