import sys
input = sys.stdin.readline

N,M=map(int,input().split())
E=[list(map(int,input().split())) for i in range(M)]

EDGE=[[] for i in range(N+1)]

for x,y,c in E:
    EDGE[x].append([y,c])
    EDGE[y].append([x,c])

MIN=[10**15]*(N+1)
MIN2=[10**15]*(N+1)

MIN[1]=0
MIN2[1]=0

from collections import deque
QUE=deque([[1,0,0]])

while QUE:
    town,dist,maxdist=QUE.popleft()
    if MIN[town]<dist and MIN2[town]<dist-maxdist:
        continue
    for to,cost in EDGE[town]:
        Flag=0
        if maxdist>cost:
            maxdist_town=maxdist
        else:
            maxdist_town=cost
            

        if MIN[to]>dist+cost:
            MIN[to]=dist+cost
            Flag=1

        if MIN2[to]>dist+cost-maxdist_town:
            MIN2[to]=dist+cost-maxdist_town
            Flag=1

        if Flag:
            QUE.append([to,dist+cost,maxdist_town])

for i in range(1,N+1):
    print(MIN[i]+MIN2[i])