#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL_DEBUG
  #include "LOCAL_DEBUG.hpp"
#endif
#define int long long
const int INF = 1LL << 60;

struct edge{ int to,cost; };
typedef tuple<int, int, int> P;

signed main(){

  int n, m; cin >> n >> m;
  vector<vector<edge>> G(n);
  for(int i = 0; i < m; i++){
    int a, b, c; cin >> a >> b >> c;
    a--, b--;
    G[a].push_back({b, c});
    G[b].push_back({a, c});
  }

  priority_queue<P,vector<P>,greater<P>> que;
  vector<vector<int>> dp(2, vector<int>(n, INF));
  dp[0][0] = dp[1][0] = 0;
  que.push({0, 0, 0}); //{最短距離,頂点}

  while( !que.empty() ){
    P p = que.top(); que.pop();
    int d = get<0>(p), u = get<1>(p), flag = get<2>(p);
    if(dp[flag][u] < d) continue;
    for(auto e : G[u]){
      if(dp[flag][e.to] > dp[flag][u] + e.cost){
        dp[flag][e.to] = dp[flag][u] + e.cost;
        que.push( {dp[flag][e.to], e.to, flag} );
      }
      if(flag == 0 && dp[1][e.to] > dp[0][u]){
        dp[1][e.to] = dp[0][u];
        que.push( {dp[1][e.to], e.to, 1} );
      }
    }
  }

  for(int i = 0; i < n; i++){
    cout << dp[0][i] + dp[1][i] << endl;
  }

  return 0;
}