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 (1.0.0) (judge verdict: Time Limit Exceeded)

import java.io.PrintWriter
import java.lang.Math.sqrt
import java.util.*

const val MOD = 1000000007L
const val INF = Long.MAX_VALUE - 1

fun main(args: Array<String>) {
    val reader = System.`in`.bufferedReader()

    val (n, q) = reader.readLine()!!.split(" ").map(Integer::parseInt)


    val edges = Array(n) {
        return@Array Edge(it)
    }

    for (i in 0 until n - 1) {
        val (a, b) = reader.readLine()!!.split(" ").map(Integer::parseInt)
        edges[a - 1].nexts.add(b - 1)
    }

    for (i in 0 until q) {
        val (p, x) = reader.readLine()!!.split(" ").map(Integer::parseInt)
        edges[p - 1].count += x
    }

    val ans = Array(n) {
        return@Array -1L
    }

    fun dfs(n: Int, ret: Long) {
        if (ans[n] != -1L) return
        val now = ret + edges[n].count
        ans[n] = now

        for (next in edges[n].nexts) {
            dfs(next, now)
        }
    }

    dfs(0, 0)

    val pw = PrintWriter(System.out)
    ans.forEach {
        pw.print("$it ")
    }
    pw.flush()
}

class Edge(var num: Int) {
    var count = 0
    val nexts = emptyList<Int>().toMutableList()
}


fun readList() = readLine()!!.split(' ')
fun readInt() = readIntList().first()
fun readIntList() = readList().map(String::toInt)
fun readLong() = readLongList().first()
fun readLongList() = readList().map(String::toLong)
fun readDoubleList() = readList().map(String::toDouble)

fun <T> readClass(n: Int, body: (List<String>) -> T): List<T> {
    val ret = mutableListOf<T>()
    for (i in 0 until n) {
        ret.add(body(readList()))
    }
    return ret
}

fun readPair(): Pair<String, String> {
    val splite = readLine()!!.split(' ')
    return Pair(splite[0], splite[1])
}

fun <T> List<T>.copy() = this.map { it }

fun Long.toBinaryString(): String {
    var t = this
    var res = ""
    while (t > 0) {
        res += (t % 2).toString()
        t /= 2
    }
    return res
}

inline fun <reified T> dualArray(h: Int, w: Int, init: (Int, Int) -> T) {
    Array(h) { i ->
        return@Array Array(w) { j ->
            return@Array init(i, j)
        }
    }
}

// 速度のためforEachは避ける
inline fun Int.rep(start: Int = 0, shiftLast: Boolean = false, body: (Int) -> Unit) {
    for (i in start until if (shiftLast) this + start else this) {
        body(i)
    }
}

inline fun Long.rep(start: Long = 0, shiftLast: Boolean = false, body: (Long) -> Unit) {
    for (i in start until if (shiftLast) this + start else this) {
        body(i)
    }
}

// 約数のList
fun divisor(value: Long): List<Long> {
    val max = sqrt(value.toDouble()).toLong()
    val former = mutableListOf<Long>()
    val latter = mutableListOf<Long>()
    (1..max).filter { value % it == 0L }
        .forEach {
            former.add(it)
            latter.add(value / it)
        }
    former.addAll(latter.reversed())
    return former
}

// 範囲内の素数を取得
// fromだけ指定すると戻り値の個数で素数判定ができる
fun prime(from: Long, to: Long = from): List<Long> {
    return (from..to).filter { i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all { j -> i % j != 0L }
    }
}

// 素因数分解
fun decom(value: Long): List<Long> {
    if (value == 1L) return listOf(1)
    val max = Math.sqrt(value.toDouble()).toLong()
    return prime(2, max).filter { value % it == 0L }
}

// 最大公約数
fun gcd(a: Long, b: Long): Long {
    return if (a % b == 0L) b else gcd(b, a % b)
}

// 文字列を入れ替え
fun swap(base: String, a: String, b: String): String {
    return base.map {
        when (it) {
            a.toCharArray()[0] -> b
            b.toCharArray()[0] -> a
            else -> it.toString()
        }
    }.joinToString()
}

// bit全探索
fun bitAllSearch(n: Int, body: (Array<Boolean>) -> Unit) {
    for (bit in 0 until (1 shl n)) {
        val s = Array(n) {
            return@Array false
        }
        for (i in 0 until n) {
            if ((bit and (1 shl i)) shr i == 1) { // i が bit に入るかどうか
                s[i] = true
            }
        }
        body(s)
    }
}

internal class UnionFindTree(size: Int) {

    private val parent = Array(size) {
        return@Array it
    }
    private val rank = Array(size) {
        return@Array 0
    }

    fun union(x: Int, y: Int): Int {
        val xRoot = find(x)
        val yRoot = find(y)

        if (xRoot == yRoot) return xRoot

        when {
            rank[xRoot] > rank[yRoot] -> parent[yRoot] = xRoot
            rank[xRoot] < rank[yRoot] -> parent[xRoot] = yRoot
            xRoot != yRoot -> {
                parent[yRoot] = xRoot
                rank[xRoot]++
            }
        }
        return parent[xRoot]
    }

    fun find(i: Int): Int {
        if (i != parent[i]) {
            parent[i] = find(parent[i])
        }
        return parent[i]
    }

    fun same(x: Int, y: Int): Boolean {
        return find(x) == find(y)
    }
}

fun <K, V> Map<K, V>.toMutableMap(): MutableMap<K, V> {
    return HashMap(this)
}