#include <iostream>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <string>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <stdio.h>
using namespace std;
#define int long long
int MOD = 1000000007;
signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	int N, M;
	cin >> N >> M;
	vector<vector<int> > g(N);
	vector<vector<int> > l(N);
	int res = 0;
	int a, b, c;
	for (int i = 0; i < M; i++) {
		cin >> a >> b >> c; a--; b--;
		g[a].push_back(b);
		g[b].push_back(a);
		l[a].push_back(c);
		l[b].push_back(c);
	}


	priority_queue < pair<int, pair<int, int> > > pq;
	int INF = (int)1 << 60;
	vector<vector<int> > dist(N, vector<int>(2, INF));

	dist[0][0] = 0;
	dist[0][1] = 0;
	pq.emplace(-dist[0][0], make_pair(0, 0));
	pq.emplace(-dist[0][1], make_pair(0, 1));

	while (pq.size() > 0) {
		a = pq.top().second.first;
		b = pq.top().second.second;
		pq.pop();

		int d = dist[a][b];

		for (int i = 0; i < g[a].size(); i++) {
			if (dist[g[a][i]][b] > d + l[a][i]) {
				dist[g[a][i]][b] = d + l[a][i];
				pq.emplace(-dist[g[a][i]][b], make_pair(g[a][i], b));
			}
			if (b == 0) {
				if (dist[g[a][i]][1] > d) {
					dist[g[a][i]][1] = d;
					pq.emplace(-dist[g[a][i]][1], make_pair(g[a][i], 1));
				}
			}
		}


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