def main():
    try:
        import sys
        sys.setrecursionlimit(10**7)
    except:
        pass
    from math import sqrt,sin,cos,tan,ceil,radians,floor,gcd,exp,log,log10,log2,factorial,fsum
    from heapq import heapify, heappop, heappush
    from bisect import bisect_left, bisect_right
    from copy import deepcopy
    import copy
    import random
    from collections import deque,Counter,defaultdict
    from itertools import permutations,combinations
    from decimal import Decimal,ROUND_HALF_UP
    #tmp = Decimal(mid).quantize(Decimal('0'), rounding=ROUND_HALF_UP)
    from functools import lru_cache, reduce
    #@lru_cache(maxsize=None)
    from operator import add,sub,mul,xor,and_,or_,itemgetter
    INF = 10**18
    mod1 = 10**9+7
    mod2 = 998244353
    
    #DecimalならPython
    
    
    '''
    
    
    
    '''
    
    N,M = map(int, input().split())
    G = [[] for _ in range(N+1)]
    for _ in range(M):
        a,b,c = map(int, input().split())
        G[a].append((b,c))
        G[b].append((a,c))
    
    Q = []
    heappush(Q,(0,1,0))
    dis = [[INF]*2 for _ in range(N+1)]
    dis[0][1] = 0
    
    while len(Q) > 0:
        cnt,pos,f = heappop(Q)
        
        if dis[pos][f] != INF:
            continue
        
        dis[pos][f] = cnt
        
        if f == 1 and dis[pos][1] >= dis[pos][0]:
            continue
        
        for nx,d in G[pos]:
            if dis[nx][f] == INF and cnt<dis[nx][0]:
                heappush(Q,(cnt+d,nx,f))
            if f == 0 and dis[nx][1] == INF and cnt<dis[nx][0]:
                heappush(Q,(cnt,nx,1))
    
    for i in range(1,N+1):
        print(dis[i][0]+min(dis[i][0],dis[i][1]))
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
if __name__ == '__main__':
    main()