from heapq import heappush, heappop
from collections import defaultdict
import sys
input = sys.stdin.readline

def dijkstra(start):
    distance = [[10**18 for _ in range(2)] for _ in range(N+1)]
    distance[start][0] = 0
    distance[start][1] = 0
    priority_queue = []
    
    heappush(priority_queue, (distance[start][0], start))
    heappush(priority_queue, (distance[start][1], start))
    
    while len(priority_queue) > 0:
        current_dist, current_node, state = heappop(priority_queue)
        
        if distance[current_node][state] < current_dist:
            continue
        
        if state == 0:
            for next_node, w in adj_dict[current_node]:
                if distance[next_node][0] > distance[current_node][0] + w:
                    distance[next_node][0] = distance[current_node][0] + w
                    heappush(priority_queue, (distance[next_node][0], next_node, 0))
                if distance[next_node][1] > distance[current_node][0]:
                    distance[next_node][1] = distance[current_node][0]
                    heappush(priority_queue, (distance[next_node][1], next_node, 1))
        else:
            for next_node, w in adj_dict[current_node]:
                if distance[next_node][1] > distance[current_node][1] + w:
                    distance[next_node][1] = distance[current_node][1] + w
                    heappush(priority_queue, (distance[next_node][1], next_node, 1))
    
    return distance

N, M = map(int, input().split())
adj_dict = defaultdict(list)

for _ in range(M):
    a_i, b_i, c_i = map(int, input().split())
    adj_dict[a_i].append((b_i, c_i))
    adj_dict[b_i].append((a_i, c_i))

distance = dijkstra(1)

for i in range(1, N+1):
    ans = distance[i][0] + distance[i][1]
    print(ans)