Problem:
Score : 400 points

Problem Statement

Given is a rooted tree with N vertices numbered 1 to N.
The root is Vertex 1, and the i-th edge (1 \leq i \leq N - 1) connects Vertex a_i and b_i.

Each of the vertices has a counter installed. Initially, the counters on all the vertices have the value 0.

Now, the following Q operations will be performed:

Operation j (1 \leq j \leq Q): Increment by x_j the counter on every vertex contained in the subtree rooted at Vertex p_j.

Find the value of the counter on each vertex after all operations.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq Q \leq 2 \times 10^5

1 \leq a_i < b_i \leq N

1 \leq p_j \leq N

1 \leq x_j \leq 10^4

The given graph is a tree.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
a_1 b_1
:
a_{N-1} b_{N-1}
p_1 x_1
:
p_Q x_Q

Output

Print the values of the counters on Vertex 1, 2, \ldots, N after all operations, in this order, with spaces in between.

Sample Input 1

4 3
1 2
2 3
2 4
2 10
1 100
3 1

Sample Output 1

100 110 111 110

The tree in this input is as follows:

Each operation changes the values of the counters on the vertices as follows:

Operation 1: Increment by 10 the counter on every vertex contained in the subtree rooted at Vertex 2, that is, Vertex 2, 3, 4. The values of the counters on Vertex 1, 2, 3, 4 are now 0, 10, 10, 10, respectively.

Operation 2: Increment by 100 the counter on every vertex contained in the subtree rooted at Vertex 1, that is, Vertex 1, 2, 3, 4. The values of the counters on Vertex 1, 2, 3, 4 are now 100, 110, 110, 110, respectively.

Operation 3: Increment by 1 the counter on every vertex contained in the subtree rooted at Vertex 3, that is, Vertex 3. The values of the counters on Vertex 1, 2, 3, 4 are now 100, 110, 111, 110, respectively.

Sample Input 2

6 2
1 2
1 3
2 4
3 6
2 5
1 10
1 10

Sample Output 2

20 20 20 20 20 20

Solution in Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn._
import scala.collection.mutable.ArrayBuffer
object Main extends App {
  val sr = new StdinReader
  val n, q = sr.nextInt

  val edges: Array[ArrayBuffer[Int]] = Array.tabulate(n + 1)(_ => new ArrayBuffer[Int]())
  (1 to n - 1).foreach {i =>
    val a, b = sr.nextInt
    edges(a) += b
    edges(b) += a
  }

  val vs = new Array[Long](n + 1)
  (1 to q).foreach {i =>
    val p, x = sr.nextInt
    vs(p) += x
  }

  def check(checks: List[Int]): Unit = {
    if (checks.nonEmpty) {
      check(checks.flatMap { i =>
        edges(i).foreach {v =>
          vs(v) += vs(i)
          edges(v) -= i
        }
        edges(i)
      })
    }
  }
  check(List(1))

  println(vs.tail.mkString(" "))
}

class StdinReader {
  val is = System.in
  val buffer = new Array[Byte](1024 * 1024)
  var size = 0
  var pos = 0

  private def readByte: Byte = {
    if (pos >= size) {
      pos = 0;
      size = is.read(buffer);
    }
    if (size < 0) -1
    else {
      val ret = buffer(pos)
      pos += 1
      ret
    }
  }

  // support single byte char only
  def next: String = {
    @scala.annotation.tailrec
    def r(sb: StringBuilder, reading: Boolean): String = {
      readByte match {
        case b if ('!' <= b && b <= '~') => r(sb.append(b.asInstanceOf[Char]), true)
        case _ => if (reading) sb.toString else r(sb, false)
      }
    }
    r(new StringBuilder, false)
  }

  def nextInt: Int = {
    @scala.annotation.tailrec
    def r(i: Int, reading: Boolean): Int = {
      readByte match {
        case '-' => r(i * -1, true)
        case b if '0' <= b && b <= '9' => r(i * 10 + (b - '0'), true)
        case _ => if (reading) i else r(i, false)
      }
    }
    r(0, false)
  }
}