#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define F first
#define S second
#define pii pair<int, int>
#define eb emplace_back
#define all(v) v.begin(), v.end()
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep3(i, l, n) for (int i = l; i < (n); ++i)
#define sz(v) (int)v.size()
#define inf (int)(1e9+7)
#define abs(x) (x >= 0 ? x : -(x))
template<typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { if (a > b) { a = b; return 1; } return 0; }
template<typename T1, typename T2> inline void chmax(T1 &a, T2 b) { if (a < b) a = b; }
template<typename T> inline T gcd(T a, T b) { if (b == 0) return a; return gcd(b, a % b); }



int n, m;
vector<vector<pair<int, ll> > > v(100005);

const ll INF = 1e18;
using P = pair<int, ll>;

vector<ll> dijkstra(int n, vector<vector<pair<int, ll> > > edge, int s) {
    vector<ll> d(n, INF);
    priority_queue<P, vector<P>, greater<P> > que; //頂点、最短距離、小さい順に
    
    
    d[s] = 0;
    que.push(P(s, 0));
    
    while (!que.empty()) {
        P p = que.top();
        que.pop();
        int cur = p.F;
        if (d[cur] < p.S) continue;
        rep(i, sz(edge[cur])) {
            int nxt = edge[cur][i].F;
            ll cost = edge[cur][i].S;
            if (d[nxt] > d[cur] + cost) {
                d[nxt] = d[cur] + cost;
                que.push(P(nxt, d[nxt]));
            }
        }
    }
    
    return d;
}

using p2 = pair<ll, pair<ll, int> >;
auto dijkstra2(int n, vector<vector<pair<int, ll> > > edge, int s) {
    vector<vector<ll> > d(n, vector<ll>(2));
    rep(i, n) rep(j, 2) d[i][j] = INF;
    d[0][0] = 0;
    d[0][1] = 0;
    
    priority_queue<p2, vector<p2>, greater<p2> > que; //頂点、最短距離、小さい順に
    
    que.push(p2(s, P(0, 0))); // 頂点, コスト, 0,1
    
    while (!que.empty()) {
        p2 p = que.top(); // 頂点, コスト
        que.pop();
        
        if (p.S.S == 0) {
            for (auto nxt : v[p.F]) {
                if (chmin(d[nxt.F][0], p.S.F + nxt.S)) { // 0 -> 0
                    que.push(p2(nxt.F, P(d[nxt.F][0], 0)));
                }
                // 0 -> 1
                if (chmin(d[nxt.F][1], p.S.F)) { // 0 -> 0
                    que.push(p2(nxt.F, P(d[nxt.F][1], 1)));
                }
            }
        } else {
            for (auto nxt : v[p.F]) {
                if (chmin(d[nxt.F][1], p.S.F + nxt.S)) { // 1 -> 1
                    que.push(p2(nxt.F, P(d[nxt.F][1], 1)));
                }
                
            }
        }
        
    }
    
    return d;
}



int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    
    cin >> n >> m;
    rep(i, m) {
        int a, b, c;
        cin >> a >> b >> c;
        a--; b--;
        v[a].eb(pii(b, c));
        v[b].eb(pii(a, c));
    }
    
    auto di = dijkstra(n, v, 0);
    // rep(i, n) cout << di[i] << " "; cout << endl;
    auto di2 = dijkstra2(n, v, 0);
    // rep(i, n) cout << di2[i][1] << " "; cout << endl;
    rep(i, n) cout << di[i] + di2[i][1] << endl;
}