#include <bits/stdc++.h>
using namespace std;
using lint = long long;
lint n, m;
typedef tuple<lint, lint, lint> P;
struct edge{lint to, cost;};
vector<vector<edge> > G;
vector<vector<lint> > dist;
const lint INF= 1e18;

void dij(int start){
	priority_queue<P, vector<P>, greater<P> > que;
	dist[0][0] = 0; dist[1][0] = 0;
	que.push(P(0, 0, 0));
	while(que.size()){
		P p = que.top(); que.pop();
		int d = get<0>(p), u = get<1>(p), flag = get<2>(p);
		if(dist[flag][u] < d) continue;
		for(auto e : G[u]){
			if(dist[flag][e.to] > dist[flag][u] + e.cost){
				dist[flag][e.to] = dist[flag][u] + e.cost;
				que.push(P(dist[flag][e.to], e.to, flag));
			}
			if(flag == 0 && dist[1][e.to] > dist[0][u]){
				dist[1][e.to] = dist[0][u];
				que.push(P(dist[1][e.to], e.to, 1));
			}
		} 
	}
}
signed main(){
	cin >> n >> m;
	G.resize(n);
	dist.resize(2, vector<lint> (n, INF));
	for(int i = 0; i < m; i++){
		lint a, b, c; cin >> a >> b >> c; --a; --b;
		G[a].push_back(edge{b, c}); G[b].push_back(edge{a, c});
	}
	dij(0);
	for(int i = 0; i < n; i++) cout << dist[0][i] + dist[1][i] << '\n';
}