#include<iostream>
#include<iomanip>
#include<limits>
#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<deque>
#include<stack>
#include<string>
#include<string.h>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#include<stdlib.h>
#include<cassert>
#include<time.h>
#include<bitset>
#include<numeric>
#include<unordered_set>
#include<unordered_map>
#include<complex>
using namespace std;
typedef long long ll;
const int mod = 1e9 + 7;
const ll infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
#define rep(i,n) for (int i=0; i < (n); i++)
typedef double D;      // 座標値の型。doubleかlong doubleを想定
typedef complex<D> P;  // Point
typedef pair<P, P> L;  // Line
typedef vector<P> VP;
typedef pair<int,int> PII;
typedef pair<ll,PII> Plii;
const D EPS = 1e-9;    // 許容誤差。問題によって変える
#define X real()
#define Y imag()
#define LE(n,m) ((n) < (m) + EPS)
#define GE(n,m) ((n) + EPS > (m))
#define EQ(n,m) (abs((n)-(m)) < EPS)
#define mkp(x,y) make_pair(x,y)
D dot(P a, P b) {
  return (conj(a)*b).X;
}
struct E{
    int t;
    ll w;
    E(int to,ll weight){
        t=to;
        w=weight;
    }
};
vector<vector<E>>G;
ll dp[100010][2];
int main(){
    cout << fixed << setprecision(10);
    int N,M;
    cin >> N >> M;
    rep(i,N)G.push_back(vector<E>());
    rep(i,M){
        int a,b;ll c;
        cin >> a >> b >> c;
        a--;b--;
        G[a].push_back(E(b,c));
        G[b].push_back(E(a,c));
    }
    rep(i,100010)rep(j,2)dp[i][j]=infll;
    dp[0][0]=dp[0][1]=0;
    priority_queue<Plii>Q;
    Q.push(mkp(0,mkp(0,0)));
    while(!Q.empty()){
        auto pl=Q.top();
        Q.pop();
        int v=pl.second.first;
        int f=pl.second.second;
        ll W=-pl.first;
        if(dp[v][f]<W)continue;
        for(auto e:G[v]){
            //no ticket
            if(dp[e.t][f]>W+e.w){
                dp[e.t][f]=W+e.w;
                Q.push(mkp(-(W+e.w),mkp(e.t,f)));
            }
            //use ticket
            if(f==false){
                if(dp[e.t][1]>W){
                    dp[e.t][1]=W;
                    Q.push(mkp(-W,mkp(e.t,1)));
                }
            }
        }
    }
    for(int i=0;i<N;i++){
        cout << dp[i][0]+dp[i][1] << "\n";
    }    
    return 0;
}