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 Kotlin (1.3.71) (judge verdict: Runtime Error)

import java.io.PrintWriter

fun main() = abc138d()

@OptIn(ExperimentalStdlibApi::class)
fun abc138d() = IO_abc138d().exec {
    val (n, q) = readLine()!!.split(' ').map { it.toInt() }

    val paths = Array(n) { mutableSetOf<Int>() }
    val values = IntArray(n)

    repeat(n - 1) {
        val (a, b) = readLine()!!.split(' ').map { it.toInt() - 1 }
        paths[a].add(b)
        paths[b].add(a)
    }

    repeat(q) {
        val (p, x) = readLine()!!.split(' ').map { it.toInt() }
        values[p - 1] += x
    }

    val visited = mutableSetOf(0)

    fun dfs(i: Int) {
        paths[i].filter { visited.add(it) }.forEach {
            values[it] += values[i]
            dfs(it)
        }
    }

    dfs(0)

    val answer = values.joinToString(" ")

    println(answer)
}

//region
@Suppress("unused", "ClassName", "SpellCheckingInspection", "ConvertToStringTemplate")
private class IO_abc138d {
    private val input = System.`in`
    private val buffer = ByteArray(1024)
    private var pointer = 0
    private var bufferLength = 0
    private val pw = PrintWriter(System.out)
    private fun Byte.isPrintable() = this in 33..126
    private fun Byte.isNumeric() = this in '0'.toByte()..'9'.toByte()
    private fun Byte.toNumVal() =
        if (this.isNumeric()) this - '0'.toByte() else error(this.toString() + " is not numeric")

    private fun hasNextByte(): Boolean {
        return if (pointer < bufferLength) true else {
            pointer = 0
            bufferLength = input.read(buffer)
            bufferLength > 0
        }
    }

    private fun readByte(): Byte = if (hasNextByte()) buffer[pointer++] else -1
    private fun skipUnprintable() = run { while (hasNextByte() && !buffer[pointer].isPrintable()) pointer++ }
    private fun hasNext(): Boolean = run { skipUnprintable() }.run { hasNextByte() }
    private fun hasNextOrError() = if (!hasNext()) error("has no next element.") else Unit

    fun readString(): String {
        hasNextOrError()
        val sb = StringBuilder()
        var b = readByte()
        while (b.isPrintable()) {
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun readLong(): Long {
        hasNextOrError()
        var n = 0L
        var negative = false
        var b = readByte()
        if (b == '-'.toByte()) {
            negative = true
            b = readByte()
        }
        if (!b.isNumeric()) error(b.toString() + " is not numeric.")
        while (true) {
            when {
                b.isNumeric() -> n = n * 10 + b.toNumVal()
                b.toInt() == -1 || !b.isPrintable() -> return if (negative) -n else n
                else -> error("failed to parse. [n=" + n + ", b=" + b + "]")
            }
            b = readByte()
        }
    }

    fun readInt() = readLong()
        .let { if (it in Int.MIN_VALUE..Int.MAX_VALUE) it.toInt() else error(it.toString() + " is not in range of Int.") }

    fun readDouble(): Double {
        var n = 0.0
        var div = 1.0
        var negative = false
        var b = readByte()
        if (b == '-'.toByte()) {
            negative = true
            b = readByte()
        }
        do n = n * 10 + b.toNumVal()
        while (run { b = readByte() }.run { b.isNumeric() })
        if (b == '.'.toByte()) {
            while (run { b = readByte() }.run { b.isNumeric() })
                n += b.toNumVal() / (run { div *= 10 }.run { div })
        }
        return if (negative) -n else n
    }

    fun readStringList(size: Int) = readList(size) { readString() }
    fun readIntList(size: Int) = readList(size) { readInt() }
    fun readLongList(size: Int) = readList(size) { readLong() }
    fun readDoubleList(size: Int) = readList(size) { readDouble() }
    fun readIntArray(size: Int) = IntArray(size) { readInt() }
    fun readLongArray(size: Int) = LongArray(size) { readLong() }
    fun readDoubleArray(size: Int) = DoubleArray(size) { readDouble() }
    inline fun <reified T> readArray(size: Int, init: () -> T) = Array(size) { init() }
    inline fun <T> readList(size: Int, init: () -> T) = List(size) { init() }
    fun println() = pw.println()
    fun print(o: Any?) = pw.print(o)
    fun println(o: Any?) = pw.println(o)
    fun exec(code: IO_abc138d.() -> Unit) = run { code() }.run { pw.flush() }
}
// endregion