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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n,m = gets.split.map(&:to_i)
g = n.times.map{[]}
m.times{
  a,b = gets.split.map(&:to_i)
  g[a-1] << b-1
  g[b-1] << a-1
}

#それぞれの頂点の距離1～10の頂点
disv = n.times.map{11.times.map{[]}}

q = [0]
used = Array.new(n,false)
tmpq = []
tmpdis = Array.new(n,0)
tmpused = Array.new(n,false)
n.times{|now|
  tmpq = [now]
  used[now] = true
  tmpdis.fill(10**9)
  tmpdis[now] = 0
  tmpused
  while tmpq.size!=0
    tn = tmpq.shift
    next if 10 <= tmpdis[tn]
    g[tn].each{|ne|
      if tmpdis[tn]+1 < tmpdis[ne]
        d = tmpdis[tn]+1
        tmpdis[ne] = d
        disv[now][d] << ne
        #disv[ne][d] << now
        tmpq << ne
      end
    }
  end
  g[now].each{|ne|
    q << ne if !used[ne]
  }
}

#
ans = Array.new(n,0)

q = gets.to_i
q.times{|i|
  v,d,c = gets.split.map(&:to_i)
  d.times{|j|
    disv[v-1][j+1].each{|w|
      ans[w] = c
    }
  }
  ans[v-1] = c
}

puts ans