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

int main() {

    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    ll N,M;
    cin>>N>>M;
    vector<vector<pair<ll,ll>>> G(N);
    for(int i=0;i<M;i++){
        ll a,b,c;
        cin>>a>>b>>c;
        a--;b--;
        G[a].push_back({b,c});
        G[b].push_back({a,c});
    }
    vector<vector<ll>> D(N,vector<ll>(2,1e18));
    D[0][0]=0;
    priority_queue<pair<ll,pair<ll,ll>>,vector<pair<ll,pair<ll,ll>>>,greater<pair<ll,pair<ll,ll>>>> Q;
    Q.push({0,{0,0}});
    vector<vector<bool>> seen(N,vector<bool>(2,0));
    while(!Q.empty()){
        ll c=Q.top().first;
        auto [n,d]=Q.top().second;
        Q.pop();
        if(seen[n][d])continue;
        seen[n][d]=1;
        for(auto [v,w]:G[n]){
            if(seen[v][d])continue;
            if(D[v][d]>c+w){
                D[v][d]=c+w;
                Q.push({c+w,{v,d}});
            }
        }
        if(d==0){
            for(auto [v,w]:G[n]){
                if(seen[v][1])continue;
                if(D[v][1]>c){
                    D[v][1]=c;
                    Q.push({c,{v,1}});
                }
            }
        }
    }
    for(int i=0;i<N;i++){
        cout<<min(D[i][0]*2,D[i][0]+D[i][1])<<endl;
    }
}