import sys
import heapq
imput = sys.stdin.readline


def dijkstra(start, g):
    INF = float("inf")
    # distance[i][j]
    # := チケットを使ってないとき(i=0)、使ったとき(i=1)のj番目まで行くときの最短距離
    distance = [[INF]*n for i in range(2)]
    distance[0][start] = 0
    distance[1][start] = 0
    cost = 0
    #q = [(距離, 現在地, チケットを使っているかどうか)]
    q = [(0, start, 0)]
    while q:
        c, v, is_used = heapq.heappop(q)
        if is_used == 1:
            if distance[1][v] < c:
                continue
            for cost, t in g[v]:
                if distance[1][v] + cost < distance[1][t]:
                    distance[1][t] = distance[1][v] + cost
                    heapq.heappush(q, (distance[1][t], t, 1))
        else:
            if distance[0][v] < c:
                continue
            for cost, t in g[v]:
                if distance[0][v] + cost < distance[0][t]:
                    distance[0][t] = distance[0][v] + cost
                    heapq.heappush(q, (distance[0][t], t, 0))
                if distance[0][v] < distance[1][t]:
                    distance[1][t] = distance[0][v]
                    heapq.heappush(q, (distance[1][t], t, 1))
    return distance


n, m = map(int, input().split())
info = tuple(tuple(map(int, input().split())) for i in range(m))
graph = [[] for i in range(n)]

for i in range(m):
    graph[info[i][0] - 1].append((info[i][2], info[i][1] - 1))
    graph[info[i][1] - 1].append((info[i][2], info[i][0] - 1))

start = 0
ans = dijkstra(start, graph)
for i in range(n):
    print(ans[0][i] + ans[1][i])