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

//repetition
#define FOR(i,a,b) for(ll i=(a);i<(b);++i)
#define rep(i, n) for(ll i = 0; i < (ll)(n); i++)

//container util
#define all(x) (x).begin(),(x).end()

//typedef
typedef long long ll;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<ll> VLL;
typedef vector<VLL> VVLL;
typedef vector<string> VS;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;

//const value
//const ll MOD = 1e9 + 7;
//const int dx[] = {0,1,0,-1};//{0,0,1,1,1,-1,-1,-1};
//const int dy[] = {1,0,-1,0};//{1,-1,0,1,-1,0,1,-1};

//conversion
inline int toInt(string s) {int v; istringstream sin(s);sin>>v;return v;}
inline ll toLL(string s) {ll v; istringstream sin(s);sin>>v;return v;}
template<class T> inline string toString(T x) {ostringstream sout;sout<<x;return sout.str();}

ll dist[100010];
ll distSkip[100010][2];
const ll INF = 1e15;
void dijkstra(int n, vector<vector<PLL>>& edge){
  rep(i,n) dist[i] = INF;
  priority_queue< PLL, vector<PLL>, greater<PLL>> que;
  que.push({0,0});
  dist[0] = 0;
  while(que.empty() == false){
    PLL p = que.top(); que.pop();
    ll c = p.first;
    ll cdist = p.second;
    if(dist[c] < cdist) continue;
    for(PLL next :edge[c]){
      if(dist[next.first] >= next.second + cdist){
        dist[next.first] = next.second + cdist;
        que.push({next.first,dist[next.first]});
      }
    }
  }
}

typedef tuple<ll,ll,ll> State;
void dijkstra_skip(int n, vector<vector<PLL>>& edge){
  rep(j,2)rep(i,n) distSkip[i][j] = INF;
  priority_queue< State, vector<State>, greater<State>> que;
  que.push({0,0,0});
  distSkip[0][0] = 0;
  distSkip[0][1] = 0;

  while(que.empty() == false){
    State p = que.top(); que.pop();
    ll c = get<0>(p);
    ll cdist = get<1>(p);
    ll flag = get<2>(p);
    if(distSkip[c][flag] < cdist) continue;
    for(PLL next :edge[c]){
      // not skip
      if(distSkip[next.first][flag] >= next.second + cdist){
        distSkip[next.first][flag] = next.second + cdist;
        que.push({next.first,distSkip[next.first][flag], flag});
      }
      // skip
      if(flag == 0 && distSkip[next.first][1] >= cdist){
        distSkip[next.first][1] =  cdist;
        que.push({next.first,distSkip[next.first][1], 1});
      }
    }
  }
}
int main(){
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n,m;
  cin >> n >> m;
  vector<vector<PLL>> edge(n);
  rep(i,m){
    ll a,b,c;
    cin >> a >> b >> c;
    a--,b--;
    edge[a].push_back({b,c});
    edge[b].push_back({a,c});
  }

  dijkstra(n,edge);
  dijkstra_skip(n,edge);
  rep(i,n){
    cout << distSkip[i][1] + dist[i] << endl;
  }
  return 0;
}