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 heapq
from collections import deque

class Node:
    def __init__(self):
        self.color = 0
        self.to = []
        self.costs = []

def fuga(graph, start, color, dist, visited):
    #print(start, dist)
    if start not in visited:
        graph[start].color = color
        visited.add(start)
    for n, c in zip(graph[start].to, graph[start].costs):
        if n in visited:
            continue
        if c > dist:
            continue
        #print("to {}, cost{}".format(n, c))
        visited.add(n)
        graph[n].color = color


def hoge(graph, start):
    visited = {start}
    q = deque(zip(graph[start].costs, graph[start].to))
    node = Node()
    while q:
        d, c = q.popleft()
        if c in visited:
            continue
        visited.add(c)
        node.to.append(c)
        node.costs.append(d)
        if d == 10:
            continue
        for n in graph[c].to:
            if n in visited:
                continue
            q.append((d+1, n))
    return node
    
def main():
    N, M = [int(i) for i in input().split()]
    graph = [Node() for _ in range(N+1)]
    for _ in range(M):
        a, b = [int(i) for i in input().split()]        
        graph[a].to.append(b)
        graph[a].costs.append(1)
        graph[b].to.append(a)
        graph[b].costs.append(1)
    ngraph = [Node()]
    for s in range(1, N+1):
        ngraph.append(hoge(graph, s))
    Q = int(input())
    queries = [[int(i) for i in input().split()] for _ in range(Q)]
    visited = set()
    for q in reversed(queries):
        v, d, c = q
        fuga(ngraph, v, c, d, visited)
    for i in range(1, N+1):
        print(ngraph[i].color)

if __name__ == "__main__":
    main()