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: Runtime Error)

n, m  = map(int, input().split())
g     = {}
used  = {i:[False for _ in range(11)] for i in range(n)}
color     = [0  for _ in range(n)]
 
for _ in range(m):
    u, v = map(int, input().split())
    u-=1
    v-=1
    if u not in g:
        g[u] = []
    if v not in g:
        g[v] = []
    g[u].append(v)
    g[v].append(u)
    
q = int(input())
Q = []
 
for _ in range(q):
    node, dis, col = map(int, input().split())
    Q.append([node-1, dis, col])
Q = Q[::-1]
 
def bfs(now, dist, col):
    if dist < 0:
        return
    
    if used[now][dist]:
        return
 
    used[now][dist] = True
    
    if not color[now]:
        color[now] = col
 
	if now in g:
    	for x in g[now]:
        	bfs(x, dist - 1, col)
            
for node, dis, col in Q:
    bfs(node, dis, col)

for x in color:
    print(x)