#include <bits/stdc++.h>
#define INF 2147483647
#define INF_LL 9223372036854775807
#define MOD 1000000007
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;

struct edge {
	ll to;
	ll cost;
};
// d v f
typedef pair<ll, pair<ll, bool>> P;

int main() {
	int N, M;
	cin >> N >> M;
	vector<vector<edge>> G(N, vector<edge>());
	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<ll> d1(N, INF), d2(N, INF), d3(N, INF);
	priority_queue<P, vector<P>, greater<P>> q, q_;
	d1[0] = 0; d2[0] = 0, d3[0] = 0;

	q.push(P{ 0,{0,false} });

	while (!q.empty()) {
		P p = q.top(); q.pop();
		ll v = p.second.first;
		for (int i = 0; i < G[v].size(); i++) {
			edge e = G[v][i];
			if (d1[e.to] > p.first + e.cost) {
				d1[e.to] = p.first + e.cost;
				q.push(P{ d1[e.to],{ e.to, p.second.second } });
			}
			if (d3[e.to] > p.first) {
				d3[e.to] = p.first;
				q_.push(P{ d3[e.to],{ e.to, true } });
			}
		}
	}
	while (!q_.empty()) {
		P p = q_.top(); q_.pop();
		ll v = p.second.first;
		if (d3[v] < p.first)continue;
		for (int i = 0; i < G[v].size(); i++) {
			edge e = G[v][i];
			if (d3[e.to] > p.first + e.cost) {
				d3[e.to] = p.first + e.cost;
				q_.push(P{ d3[e.to],{ e.to, p.second.second } });
			}
		}
	}

	for (int i = 0; i < N; i++) {
		cout << min(d3[i] + d1[i],d1[i]*2) << endl;
	}
}