import heapq
N,M = map(int,input().split())
lsg = [[] for i in range(N)]
for i in range(M):
    a,b,c = map(int,input().split())
    a -= 1
    b -= 1
    lsg[a].append((b,c))
    lsg[b].append((a,c))

h = [(0,0,0)]
INF = float('INF')
cost0 = [INF]*(N)
cost1 = [INF]*(N)
cost0[0] = 0
cost1[0] = 0
used0 = [False]*(N)
used1 = [False]*(N)
while h:
    c,n,f = heapq.heappop(h)
    if used0[n] and used1[n]:
        continue
    if f == 0:
        used0[n] = True
    if f == 1:
        used1[n] = True
    for nex,cos in lsg[n]:
        if f == 0: # 使える
            if used0[nex]==False:
                if cost0[nex] > c + cos: # 使わない
                    cost0[nex] = c + cos
                    heapq.heappush(h, (c+cos,nex,0))
            if used1[nex]==False:
                if cost1[nex] > c: # 使う
                    cost1[nex] = c
                    heapq.heappush(h, (c,nex,1))
        if f == 1: # 使えない
            if used1[nex]==False:
                if cost1[nex] > c+ cos:
                    cost1[nex] = c+ cos
                    heapq.heappush(h, (c+ cos,nex,1))

for i in range(N):
    print(cost0[i]+cost1[i])