typedef long long ll;
#include <bits/stdc++.h>
using namespace std;
template<typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val){
    std::fill( (T*)array, (T*)(array+N), val );
}
typedef pair<ll, ll> P;
struct edge {
    ll to;
    ll cost;
};
vector<edge> G[100010];
int main() {
    ll n,m;
    std::cin >> n>>m;
    ll d[100010];
    ll inf = 100000000000000+10;
    Fill(d,inf);
    d[0] = 0;
    for (int i = 0; i < m; i++) {
        ll tmp_a,tmp_b,tmp_c;
        std::cin >> tmp_a>>tmp_b>>tmp_c;
        tmp_a--;
        tmp_b--;
        edge e1 = {tmp_b,tmp_c};
        edge e2 = {tmp_a,tmp_c};
        G[tmp_a].push_back(e1);
        G[tmp_b].push_back(e2);
    }
    
    priority_queue<P, vector<P>, greater<P> > que;
    que.push(P(0, 0));
    
    ll logest[100010];
    Fill(logest,0);
    
    while (!que.empty()) {
        P p = que.top();
        que.pop();
        int v = p.second;
        if (d[v] < p.first) continue;

        for (int i=0; i<G[v].size(); ++i) {
            edge e = G[v][i];
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                // logest[e.to] = max({logest[e.to],logest[v],e.cost});
                // std::cout << logest[e.to] << std::endl;
                que.push(P(d[e.to], e.to));
            }
        }
    }
    
    // 最大距離消えるバージョン
    ll d2[100010];
    Fill(d2,inf);
    d2[0] = 0;
    priority_queue<P, vector<P>, greater<P> > que2;
    que2.push(P(0,0));
    while (!que2.empty()) {
        P p = que2.top();
        que2.pop();
        int v = p.second;
        if (d2[v] < p.first) continue;

        for (int i=0; i<G[v].size(); ++i) {
            edge e = G[v][i];
            ll now_longest = max( logest[v], e.cost );
            if (d2[e.to] > d2[v] + e.cost - now_longest + logest[v]) {
                d2[e.to] = d2[v] + e.cost - now_longest + logest[v];
                logest[e.to] = max({logest[e.to],now_longest});
                // std::cout << logest[e.to] << std::endl;
                que2.push(P(d2[e.to], e.to));
            }
        }
    }
    
    for (int i = 0; i < n; i++) {
        std::cout << d[i]+d2[i]<< std::endl;
    }
}