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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

data class Manipulation(val v: Int, val d: Int, val c: Int)

fun main(args: Array<String>) {
    val (n, m) = readLine()!!.split(" ").map(String::toInt)
    val connections = Array<MutableSet<Int>>(n) { mutableSetOf() }
    (1..m).forEach {
        val (a, b) = readLine()!!.split(" ").map(String::toInt)
        connections[a - 1].add(b)
        connections[b - 1].add(a)
    }
    val q = readLine()!!.toInt()
    val manipulations = (1..q).map {
        val (v, d, c) = readLine()!!.split(" ").map(String::toInt)
        Manipulation(v, d, c)
    }

    val vertexes = Array(n) { 0 }
    manipulations.forEach {
        manipulation ->
        manipulate(manipulation, connections, vertexes)
    }

    vertexes.forEach(::println)
}

fun manipulate(manipulation: Manipulation, connections: Array<MutableSet<Int>>, vertexes: Array<Int>) {
    if (manipulation.d < 0) {
        return
    }
    vertexes[manipulation.v - 1] = manipulation.c
    connections[manipulation.v - 1].forEach { v ->
        val m = Manipulation(v, manipulation.d - 1, manipulation.c)
        manipulate(m, connections, vertexes)
    }
}