Problem:
Score : 700 points

Problem Statement

Squid loves painting vertices in graphs.

There is a simple undirected graph consisting of N vertices numbered 1 through N, and M edges.
Initially, all the vertices are painted in color 0. The i-th edge bidirectionally connects two vertices a_i and b_i. The length of every edge is 1.

Squid performed Q operations on this graph. In the i-th operation, he repaints all the vertices within a distance of d_i from vertex v_i, in color c_i.

Find the color of each vertex after the Q operations.

Constraints

1 ≤ N,M,Q ≤ 10^5

1 ≤ a_i,b_i,v_i ≤ N

a_i ≠ b_i

0 ≤ d_i ≤ 10

1 ≤ c_i ≤10^5

d_i and c_i are all integers.

There are no self-loops or multiple edges in the given graph.

Partial Score

200 points will be awarded for passing the testset satisfying 1 ≤ N,M,Q ≤ 2{,}000.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_{M} b_{M}
Q
v_1 d_1 c_1
:
v_{Q} d_{Q} c_{Q}

Output

Print the answer in N lines.
In the i-th line, print the color of vertex i after the Q operations.

Sample Input 1

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2

Sample Output 1

2
2
2
2
2
1
0

Initially, each vertex is painted in color 0.
In the first operation, vertices 5 and 6 are repainted in color 1.
In the second operation, vertices 1, 2, 3, 4 and 5 are repainted in color 2.

Sample Input 2

14 10
1 4
5 7
7 11
4 10
14 7
14 3
6 14
8 11
5 13
8 3
8
8 6 2
9 7 85
6 9 3
6 7 5
10 3 1
12 9 4
9 6 6
8 2 3

Sample Output 2

1
0
3
1
5
5
3
3
6
1
3
4
5
3

The given graph may not be connected.

Solution in PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
input = lambda : sys.stdin.readline().rstrip()
sys.setrecursionlimit(max(1000, 10**9))
write = lambda x: sys.stdout.write(x+"\n")

n,m = list(map(int, input().split()))
from collections import defaultdict
ns = defaultdict(list)
for _ in range(m):
    u,v = map(int, input().split())
    u -= 1
    v -= 1
    ns[u].append(v)
    ns[v].append(u)
    
dp = [[-1]*n for _ in range(11)]
q = int(input())
qs = [None]*q
for i in range(q):
    v,d,c = tuple(map(int, input().split()))
    v -= 1
    qs[i] = (i,v,d,c)
    dp[d][v] = i
from itertools import product
for i,u in product(range(10,0,-1), range(n)):
    if dp[i][u]>=0:
        dp[i-1][u] = max(dp[i-1][u], dp[i][u])
        for v in ns[u]:
            dp[i-1][v] = max(dp[i-1][v], dp[i][u])

write("\n".join(map(str, ((qs[dp[0][u]][3] if dp[0][u]>=0 else 0) for u in range(n)))))