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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import java.io._
import java.util.StringTokenizer

import scala.collection.mutable
import scala.util.Sorting
import math.{abs, max, min}
import scala.collection.mutable.ArrayBuffer
import scala.reflect.ClassTag

object Main {
  val MOD = 1000000007
  val out = new PrintWriter(System.out)

  def solve(): Unit = {
    val sc = new InputReader(System.in)
    val N, M = sc.nextInt()
    val g = Array.fill[mutable.Map[Int, Int]](N)(mutable.Map())
    rep(M){ _ =>
      val a, b = sc.nextInt() - 1
      g(a) += b -> 0
      g(b) += a -> 0
    }

    val C = Array.ofDim[Int](N)
    case class Op(v: Int, d: Int, c: Int)
    val Q = sc.nextInt()
    val ops = map(Q){ _ =>
      val v, d, c = sc.nextInt()
      Op(v - 1, d, c)
    }

    def wfs(q: mutable.Queue[Int], d: Int, c: Int, visit: mutable.Set[Int]): Unit = {
      if (d == 0) ()
      else {
        val next = mutable.Queue[Int]()
        while (q.nonEmpty) {
          val v = q.dequeue()
          g(v) foreach { case (u, d1) =>
            if (!(visit contains u) && d1 < d) {
              if (C(u) == 0) C(u) = c
              g(v)(u) = d
              visit += u
              next.enqueue(u)
            }
          }
        }

        wfs(next, d - 1, c, visit)
      }
    }

    rep_r(Q) { i =>
      val op = ops(i)
      if (C(op.v) == 0) C(op.v) = op.c
      wfs(mutable.Queue(op.v), op.d, op.c, mutable.Set())
    }

    rep(N)(i => out.println(C(i)))
  }

  def main(args: Array[String]): Unit = {
    solve()
    out.flush()
  }


  class InputReader(val stream: InputStream) {
    private val reader = new BufferedReader(new InputStreamReader(stream), 32768)
    private var tokenizer: StringTokenizer = null

    def next(): String = {
      while (tokenizer == null || !tokenizer.hasMoreTokens)
        tokenizer = new StringTokenizer(reader.readLine)
      tokenizer.nextToken
    }

    def nextInt(): Int = next().toInt
    def nextLong(): Long = next().toLong
    def nextChar(): Char = next().charAt(0)
  }
  def rep(n: Int)(f: Int => Unit): Unit = {
    var i = 0
    while(i < n) { f(i); i += 1 }
  }
  def rep_r(n: Int)(f: Int => Unit): Unit = {
    var i = n - 1
    while(i >= 0) { f(i); i -= 1 }
  }

  def map[@specialized A: ClassTag](n: Int)(f: Int => A): Array[A] = {
    val res = Array.ofDim[A](n)
    rep(n)(i => res(i) = f(i))
    res
  }

  implicit class ArrayOpts[A](val as: Array[A]) extends AnyVal {
    // todo Orderingだとboxing発生するので自作Orderを用意したい
    def maxByOpt[B: Ordering](f: A => B): Option[A] = {
      if (as.nonEmpty) Some(as.maxBy(f)) else None
    }

    def grpBy[K](f: A => K): mutable.Map[K, ArrayBuffer[A]] = {
      val map = mutable.Map.empty[K, ArrayBuffer[A]]
      rep(as.length)(i => map.getOrElseUpdate(f(as(i)), ArrayBuffer()) += as(i))
      map
    }

    def sumBy[B](f: A => B)(implicit num: Numeric[B]): B = {
      var sum = num.zero
      rep(as.length)(i => sum = num.plus(sum, f(as(i))))
      sum
    }

    def minByEx[B](f: A => B, ixRange: Range = as.indices)(implicit cmp: Ordering[B]): (A, B) = {
      limit(f, ixRange)(cmp.lt)
    }

    def maxByEx[B](f: A => B, ixRange: Range = as.indices)(implicit cmp: Ordering[B]): (A, B) = {
      limit(f, ixRange)(cmp.gt)
    }

    private def limit[B](f: A => B, ixRange: Range)(cmp: (B, B) => Boolean): (A, B) = {
      var limA = as(ixRange.head)
      var limB = f(limA)

      for (i <- ixRange.tail) {
        val a = as(i)
        val b = f(a)
        if (cmp(b, limB)) {
          limA = a
          limB = b
        }
      }
      (limA, limB)
    }
  }

  implicit class IterableOpts[A](val as: Iterable[A]) extends AnyVal {
    def sumBy[B](f: A => B)(implicit num: Numeric[B]): B = {
      as.foldLeft(num.zero)((acc, a) => num.plus(acc, f(a)))
    }
  }
}