#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <string>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <deque>
#include <numeric>
#include <bitset>
#include <iomanip>
#include <cassert>
#include <chrono>
#include <random>
#include <limits>
#include <iterator>
#include <functional>
#include <sstream>
#include <complex>
using namespace std;

typedef long long ll;
typedef uint64_t ull;
typedef pair<int, int> P;
typedef pair<int, double> Pid;
typedef pair<double, int> Pdi;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<int, pair<int, int>> PP;
typedef pair<P, int> PPi;
constexpr double PI = 3.1415926535897932;   // acos(-1)
constexpr double EPS = 1e-9;
constexpr int INF = 1001001001;
constexpr int mod = 1000000007;
// constexpr int mod = 998244353;

#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
#define chadd(x, y) x = (x + y) % mod

struct Edge{
    int to, cost;
    Edge() = default;
    Edge(int to, int cost) : to(to), cost(cost) {}
};

struct Info{
    ll dist;
    int longest, v;
    Info() = default;
    Info(ll d, int l, int v) : dist(d), longest(l), v(v) {}
    bool operator<(const Info& info) const{
        if(dist == info.dist){
            return longest > info.longest;
        }
        return dist < info.dist;
    }
    bool operator>(const Info& info) const{
        return !((*this) < info);
    }
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int n, m;
    cin >> n >> m;
    vector<vector<Edge>> graph(n);
    vector<ll> dist(n, 1e+17), dist2(n, 1e+17);
    for(int i = 0; i < m; ++i){
        int a, b, c;
        cin >> a >> b >> c;
        --a, --b;
        graph[a].emplace_back(Edge(b, c));
        graph[b].emplace_back(Edge(a, c));
    }

    priority_queue<Pl, vector<Pl>, greater<Pl>> que;
    dist[0] = 0;
    que.push(Pl(0, 0));
    while(!que.empty()){
        Pl p = que.top();
        que.pop();
        ll d = p.first;
        int from = p.second;
        if(d > dist[from])  continue;
        for(Edge e : graph[from]){
            int to = e.to, cost = e.cost;
            if(dist[to] > d + cost){
                dist[to] = d + cost;
                que.push(Pl(dist[to], to));
            }
        }
    }
    
    priority_queue<Info, vector<Info>, greater<Info>> que2;
    dist2[0] = 0;
    que2.push(Info(0, 0, 0));
    while(!que2.empty()){
        Info p = que2.top();
        que2.pop();
        ll d = p.dist;
        int longest = p.longest, from = p.v;
        if(d > dist2[from]) continue;
        for(Edge e : graph[from]){
            int to = e.to, cost = e.cost;
            if(longest >= cost){
                if(dist2[to] > d + cost){
                    dist2[to] = d + cost;
                    que2.push(Info(dist2[to], longest, to));
                }
            }
            else{
                if(dist2[to] > d + longest){
                    dist2[to] = d + longest;
                    que2.push(Info(dist2[to], cost, to));
                }
            }
        }
    }
    for(int i = 0; i < n; ++i)  cout << dist[i] + dist2[i] << "\n";
}