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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import numpy as np

nodeid = 0

class node():
    def __init__(self):
        global nodeid
        self.neighbor = []
        self.color = 0
        self.id = nodeid
        nodeid += 1
    def add(self, new_neighbor):
        self.neighbor.append(new_neighbor)
    def draw(self, p, d, color):
        if d < 0:
            return
        if self.color == 0:
            #print("node[{}] <- {}".format(self.id, color))
            self.color = color
        for n in self.neighbor:
            if p is n:
                continue
            n.draw(self, d-1, color)

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

nodes = [node() for i in range(N)]
for i in range(M):
    a, b = list(map(int, input().split()))
    nodes[a-1].add(nodes[b-1])
    nodes[b-1].add(nodes[a-1])

Q = int(input())

operation = []
for i in range(Q):
    v, d, c = list(map(int, input().split()))
    operation.append([v, d, c])

operation.reverse()
super = node()
for op in operation:
    #print("op: v={}, c={}, d={}".format(op[0], op[1], op[2]))
    nodes[op[0]-1].draw(super, op[1],op[2])

for n in nodes:
    print(n.color)