#include <iostream>
#include <queue>
#include <tuple>
#include <vector>
using namespace std;
using i64 = int64_t;

struct edge { int to; i64 cost; };
constexpr i64 inf = 987'654'321'987'654'321;

template <class T>
void readint(T *x) {
  *x = 0;
  int c;
  for(;;) {
    c = getchar_unlocked();
    switch(c) case 48: case 49: case 50: case 51: case 52: case 53: case 54: case 55: case 56: case 57: goto num;
  }

num:
  for(;;) {
    switch(c) {
      case 48: case 49: case 50: case 51: case 52: case 53: case 54: case 55: case 56: case 57:
        *x *= 10;
        *x += c - 48;
        break;
      default:
        return;
    }
    c = getchar_unlocked();
  }
}

int main(void) {
  int N, M; readint(&N); readint(&M);
  vector<vector<edge>> G(N, vector<edge>());
  for(int i=0; i<M; ++i) {
    int a, b, c; readint(&a); readint(&b); readint(&c);
    --a, --b;
    G[a].push_back(edge{b, c});
    G[b].push_back(edge{a, c});
  }
  // cost[頂点][チケットを使ったか] := 最小コスト
  vector<vector<i64>> cost(N, vector<i64>(2, inf));
  cost[0][0] = 0;
  cost[0][1] = 0;
  vector<vector<bool>> seen(N, vector<bool>(2, false));
  // コスト、頂点、チケットを使ったか
  priority_queue<tuple<i64, int, bool>, vector<tuple<i64, int, bool>>, greater<tuple<i64, int, bool>>> pq;
  pq.emplace(0, 0, false);
  while(!pq.empty()) {
    auto [_, v, used] = pq.top(); pq.pop();
    if(seen[v][used]) { continue; }
    seen[v][used] = true;
    for(edge &e : G[v]) {
      // チケットを使わない
      if(cost[e.to][used] > cost[v][used] + e.cost) {
        cost[e.to][used] = cost[v][used] + e.cost;
        pq.emplace(cost[e.to][used], e.to, used);
      }
      // チケットを使う
      if(!used && cost[e.to][true] > cost[v][false]) {
        cost[e.to][true] = cost[v][false];
        pq.emplace(cost[e.to][true], e.to, true);
      }
    }
  }
  for(int v=0; v<N; ++v) {
    printf("%ld\n", cost[v][true] + cost[v][false]);
  }
  return 0;
}