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 (2.4.0) (judge verdict: Time Limit Exceeded)

import collections

if __name__ == '__main__':
    n, m = map(int, input().split())

    routes = collections.defaultdict(list)
    for _ in range(m):
        a, b = (int(x) - 1 for x in input().split())
        routes[a].append(b)
        routes[b].append(a)

    matrix = [[None for _ in range(n)] for _ in range(n)]
    for i in range(n):
        cnt = 1
        buffer = set([i])
        matrix[i][i] = 0

        while buffer and not all(matrix[i]):
            temp = set()
            for x in buffer:
                for j in routes[x]:
                    if matrix[i][j] is None:
                        matrix[i][j] = cnt
                        temp.add(j)

            buffer = temp
            cnt += 1

    colors = [0 for _ in range(n)]
    q = int(input())
    for _ in range(q):
        v, d, c = map(int, input().split())
        v -= 1

        for w in range(n):
            if matrix[v][w] is not None and matrix[v][w] <= d: colors[w] = c

    for color in colors: print(color)