import sys
import heapq

def main():
    input = sys.stdin.read().split()
    ptr = 0
    N = int(input[ptr])
    ptr += 1
    M = int(input[ptr])
    ptr += 1

    adj = [[] for _ in range(N + 1)]
    for _ in range(M):
        a = int(input[ptr])
        ptr += 1
        b = int(input[ptr])
        ptr += 1
        c = int(input[ptr])
        ptr += 1
        adj[a].append((b, c))
        adj[b].append((a, c))

    # Initialize distances
    INF = float('inf')
    d0 = [INF] * (N + 1)
    d0[1] = 0
    d1 = [INF] * (N + 1)

    heap = []
    heapq.heappush(heap, (0, 1, 0))  # (distance, node, state)

    while heap:
        dist, u, s = heapq.heappop(heap)
        if s == 0 and dist > d0[u]:
            continue
        if s == 1 and dist > d1[u]:
            continue
        for v, c in adj[u]:
            if s == 0:
                # Not using ticket
                new_dist = dist + c
                if new_dist < d0[v]:
                    d0[v] = new_dist
                    heapq.heappush(heap, (new_dist, v, 0))
                # Using ticket
                new_dist = dist + 0
                if new_dist < d1[v]:
                    d1[v] = new_dist
                    heapq.heappush(heap, (new_dist, v, 1))
            else:
                # Using ticket already
                new_dist = dist + c
                if new_dist < d1[v]:
                    d1[v] = new_dist
                    heapq.heappush(heap, (new_dist, v, 1))

    for i in range(1, N + 1):
        if d0[i] == INF:
            print(0)
        else:
            option1 = 2 * d0[i]
            option2 = d1[i] + d0[i] if d1[i] != INF else INF
            option3 = d0[i] + d1[i] if d1[i] != INF else INF
            min_option = min(option1, option2, option3)
            print(min_option)

if __name__ == '__main__':
    main()