from heapq import heapify as hpi , heappop as hpop , heappush as hpush
n,m=map(int,input().split())
g = [[] for i in range(n)]
for _ in range(m):
    x,y,z = map(int,input().split())
    x-=1
    y-=1
    g[x].append((y,z))
    g[y].append((x,z))

inf=float('inf')
d = [[inf,inf] for i in range(n)]
d[0][0] = 0
d[0][1] = 0
done=[[0,0] for i in range(n)]
hp=[]

def  daiku(i,f):
    hpush(hp,(d[i][f],i,f))
    
    while hp:
        _ ,now,ch= hpop(hp)
        if done[now][ch]:
            continue
            
        done[now][ch] = 1
    
        for go,cost in g[now]:
            if d[go][ch] > d[now][ch] + cost:
                d[go][ch] = d[now][ch] + cost
                hpush(hp,(d[go][ch],go,ch))
            if ch == 0:
                if d[go][ch+1] > d[now][ch]:
                    d[go][ch+1] = d[now][ch]
                    hpush(hp,(d[go][ch+1],go,ch+1))
            
daiku(0,0)
for i in range(n):
    print(d[i][0] + d[i][1])