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: Runtime Error)

@file:Suppress("DuplicatedCode")

import java.io.IOException
import java.io.InputStream
import java.io.PrintWriter
import java.util.*

fun main(args: Array<String>) {
    PrintWriter(System.out).use { out ->
        D.solve(D.FastScanner(), out)
        out.flush()
    }
}

private fun D.solve(sc: D.FastScanner, out: PrintWriter) {
    val n = sc.nextInt()
    val q = sc.nextInt()

    val nodeList = Array(n) { D.BitSet(n) }
    repeat(n - 1) {
        val a = sc.nextInt() - 1
        val b = sc.nextInt() - 1
        nodeList[a][b] = true
        nodeList[b][a] = true
    }

    val counter = IntArray(n)
    repeat(q) {
        val index = sc.nextInt() - 1
        counter[index] += sc.nextInt()
    }
    val visited = D.BitSet(n)
    val queue = ArrayDeque(listOf(0 to 0))

    while (queue.isNotEmpty()) {
        val (current, sum) = queue.removeFirst()
        visited[current] = true
        counter[current] += sum
        nodeList[current].trueIterator().forEach {
            if (!visited[it]) {
                queue.add(it to counter[current])
            }
        }
    }

    counter.forEach {
        println(it)
    }
}

@Suppress("MemberVisibilityCanBePrivate")
private object D {
    private const val zeroCode = '0'.toInt()
    private const val nineCode = '9'.toInt()

    class FastScanner {
        private val `in`: InputStream = System.`in`
        private val buffer = ByteArray(1024)
        private var ptr = 0
        private var buflen = 0
        private fun hasNextByte(): Boolean {
            if (ptr < buflen) {
                return true
            } else {
                ptr = 0
                try {
                    buflen = `in`.read(buffer)
                } catch (e: IOException) {
                    e.printStackTrace()
                }
                if (buflen <= 0) {
                    return false
                }
            }
            return true
        }

        private fun readByte(): Int {
            return if (hasNextByte()) buffer[ptr++].toInt() else -1
        }

        operator fun hasNext(): Boolean {
            while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
            return hasNextByte()
        }

        operator fun next(): String {
            if (!hasNext()) throw NoSuchElementException()

            return buildString {
                var b = readByte()

                while (isPrintableChar(b)) {
                    appendCodePoint(b)
                    b = readByte()
                }
            }
        }

        fun nextLong(): Long {
            if (!hasNext()) throw NoSuchElementException()
            var n: Long = 0
            var minus = false
            var b = readByte()

            if (b == '-'.toInt()) {
                minus = true
                b = readByte()
            }

            if (b !in zeroCode..nineCode) {
                throw NumberFormatException()
            }

            while (true) {
                if (b in zeroCode..nineCode) {
                    n *= 10
                    n += b - zeroCode.toLong()
                } else if (b == -1 || !isPrintableChar(b)) {
                    return if (minus) -n else n
                } else {
                    throw NumberFormatException()
                }

                b = readByte()
            }
        }

        fun nextInt(): Int {
            val nl = nextLong()
            if (nl < Int.MIN_VALUE || nl > Int.MAX_VALUE) throw NumberFormatException()
            return nl.toInt()
        }

        fun nextDouble(): Double {
            return next().toDouble()
        }

        fun readIntArray(n: Int): IntArray {
            val arr = IntArray(n)

            for (i in 0 until n) {
                arr[i] = nextInt()
            }

            return arr
        }

        fun readBigInt(capacity: Int): IntArray {
            if (!hasNext()) throw NoSuchElementException()

            val arr = IntArray(capacity)
            var len = 0
            arr[0] = readByte() - zeroCode
            while (arr[len] in 0..9) {
                len++
                arr[len] = readByte() - zeroCode
            }

            return arr.sliceArray(0 until len)
        }

        companion object {
            private fun isPrintableChar(c: Int): Boolean {
                return c in 33..126
            }
        }
    }

    class BitSet(capacity: Int) {
        val bitset = java.util.BitSet(capacity)

        val cardinality: Int
            get() = bitset.cardinality()

        override fun equals(other: Any?) = (other as? BitSet)?.let { it.bitset == bitset } ?: false

        operator fun set(n: Int, f: Boolean) {
            if (f) {
                bitset.set(n)
            } else {
                bitset.clear(n)
            }
        }

        operator fun get(n: Int) = bitset[n]

        fun trueIterator(startIndex: Int = 0) = object: IntIterator() {
            var nextPos = bitset.nextSetBit(startIndex)

            override fun hasNext() = nextPos in 0 until Int.MAX_VALUE

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.nextSetBit(nextPos + 1)
                return value
            }
        }

        fun falseIterator(startIndex: Int = 0) = object: IntIterator() {
            var nextPos = bitset.nextClearBit(startIndex)

            override fun hasNext() = nextPos in 0 until Int.MAX_VALUE

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.nextClearBit(nextPos + 1)
                return value
            }
        }

        fun trueIteratorReversed(startIndex: Int = bitset.length() - 1) = object: IntIterator() {
            var nextPos = bitset.previousSetBit(startIndex)

            override fun hasNext() = nextPos >= 0

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.previousSetBit(nextPos - 1)
                return value
            }
        }

        fun falseIteratorReversed(startIndex: Int = bitset.length() - 1) = object: IntIterator() {
            var nextPos = bitset.previousClearBit(startIndex)

            override fun hasNext() = nextPos >= 0

            override fun nextInt(): Int {
                val value = nextPos
                nextPos = bitset.previousClearBit(nextPos - 1)
                return value
            }
        }

        fun and(other: BitSet) {
            bitset.and(other.bitset)
        }

        fun or(other: BitSet) {
            bitset.or(other.bitset)
        }

        fun xor(other: BitSet) {
            bitset.xor(other.bitset)
        }

        fun andNot(other: BitSet) {
            bitset.andNot(other.bitset)
        }
    }
}