import sys, re
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians
from itertools import accumulate, permutations, combinations, product
from operator import itemgetter, mul, add
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits
from bisect import bisect, bisect_left
from fractions import gcd
from heapq import heappush, heappop
from functools import reduce
from decimal import Decimal, getcontext
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(): return list(map(int, input().split()))
def ZIP(n): return zip(*(MAP() for _ in range(n)))
sys.setrecursionlimit(10 ** 9)
INF = float('inf')
mod = 10 ** 9 + 7

N, M = MAP()
graph = [[] for _ in range(N)]

def ticketdijkstra(E, start):
	N_d = len(E)
	dist = [[INF]*2 for _ in range(N_d)]
	dist[start][0] = 0
	dist[start][1] = 0
	q = [(0, start, 0)]
	while q:
		dist_v, v, use_ticket = heappop(q)
		if dist[v][0] != dist_v and dist[v][1] != dist_v:
			continue
		for u, dist_vu in E[v]:
			if use_ticket:
				dist_u = dist_v + dist_vu
				if dist_u < dist[u][1]:
					dist[u][1] = dist_u
					heappush(q, (dist_u, u, 1))
			else:
				dist_u = dist_v + dist_vu
				if dist_u < dist[u][0]:
					dist[u][0] = dist_u
					heappush(q, (dist_u, u, 0))
				dist_u = dist_v
				if dist_u < dist[u][1]:
					dist[u][1] = dist_u
					heappush(q, (dist_u, u, 1))

	return dist


for _ in range(M):
	a, b, c = MAP()
	graph[a-1].append((b-1, c))
	graph[b-1].append((a-1, c))

d = ticketdijkstra(graph, 0)

for i in range(N):
	print(d[i][0]+d[i][1])