import sys
import heapq

def main():
    input = sys.stdin.read
    data = input().split()
    idx = 0
    N = int(data[idx])
    idx += 1
    M = int(data[idx])
    idx += 1
    
    adj = [[] for _ in range(N+1)]
    for _ in range(M):
        a = int(data[idx])
        idx += 1
        b = int(data[idx])
        idx += 1
        c = int(data[idx])
        idx += 1
        adj[a].append((b, c))
        adj[b].append((a, c))
    
    INF = float('inf')
    dist = [[INF] * 2 for _ in range(N+1)]
    dist[1][0] = 0
    heap = []
    heapq.heappush(heap, (0, 1, 0))
    
    while heap:
        d, u, s = heapq.heappop(heap)
        if d > dist[u][s]:
            continue
        for v, c in adj[u]:
            if s == 0:
                if dist[v][0] > d + c:
                    dist[v][0] = d + c
                    heapq.heappush(heap, (dist[v][0], v, 0))
                if dist[v][1] > d:
                    dist[v][1] = d
                    heapq.heappush(heap, (dist[v][1], v, 1))
            else:
                if dist[v][1] > d + c:
                    dist[v][1] = d + c
                    heapq.heappush(heap, (dist[v][1], v, 1))
    
    for i in range(1, N+1):
        if i == 1:
            print(0)
            continue
        d0 = dist[i][0]
        d1 = dist[i][1]
        min_dist = min(2 * d0, d0 + d1)
        print(min_dist)

if __name__ == "__main__":
    main()