import sys

sys.setrecursionlimit(10**6)
int1 = lambda x: int(x)-1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.buffer.readline())
def FI(): return float(sys.stdin.buffer.readline())
def MI(): return map(int, sys.stdin.buffer.readline().split())
def MF(): return map(float, sys.stdin.buffer.readline().split())
def MI1(): return map(int1, sys.stdin.buffer.readline().split())
def LI(): return list(map(int, sys.stdin.buffer.readline().split()))
def LI1(): return list(map(int1, sys.stdin.buffer.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def BI(): return sys.stdin.buffer.readline().rstrip()
def SI(): return sys.stdin.buffer.readline().rstrip().decode()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
inf = 10**16
# md = 998244353
md = 10**9+7

from heapq import *

n, m = MI()
to = [[] for _ in range(n)]
for _ in range(m):
    u, v, c = MI1()
    to[u].append((v, c+1))
    to[v].append((u, c+1))

dist = [inf]*n*2
dist[0] = 0
dist[1] = 0
hp = [(0, 0)]
while hp:
    d, u = heappop(hp)
    if d > dist[u]: continue
    u, f = divmod(u, 2)
    for v, c in to[u]:
        nd, nv = d+c, v*2+f
        if nd < dist[nv]:
            dist[nv] = nd
            heappush(hp, (nd, nv))
        if f == 0:
            nd, nv = d, v*2+1
            if nd < dist[nv]:
                dist[nv] = nd
                heappush(hp, (nd, nv))

for u in range(n):
    print(dist[u*2]+dist[u*2+1])