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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder2 {
	class Program {
		static void Main(string[] args) {

			//出力の都度更新をやめる
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);


			Ans();

			//更新する
			Console.Out.Flush();
			
		}
public static void Ans() {

			var inputArray = retreiveLongArray();
			var inputCount = 2;

			// 不正な入力は処理しない
			if (inputArray.Length != inputCount) {
				Console.WriteLine("invalid input");
				return;
			}
			long N = inputArray[0];
			long Q = inputArray[1];

			var hens = createLongTuppleList(N-1);
			var nums = createLongTuppleList(Q);

			var countDic = new Dictionary<long, long>();
			
			for (int i = 1; i <= N; i++) {
				countDic.Add(i, 0);
			}
			
			for (int i = 0; i < Q; i++) {
				var num = nums[i];
				countDic[num.Item1] += num.Item2;
			}


			//treeの構造を作成する
			_tree = new Dictionary<long, List<long>>();
			for (int i = 1; i <= N; i++) {
				_tree.Add(i, new List<long>());
			}
			for (int i = 0; i < N-1; i++) {
				var hen = hens[i];
				_tree[hen.Item1].Add(hen.Item2);
				_tree[hen.Item2].Add(hen.Item1);
			}
			
			_ansDic = new Dictionary<long, long>();
			for (int i = 1; i <= N; i++) {
				_ansDic.Add(i, 0);
			}

			_countDic = countDic;
			DFS(1,0,-1);

			for (int i = 1; i <= N; i++) {
				Console.WriteLine(_ansDic[i]);
			}

			//答えの出力
			var ans = "";
			Console.WriteLine(ans);

		}

		private static Dictionary<long, long> _ansDic;
		private static Dictionary<long, List<long>> _tree;
		private static Dictionary<long, long> _countDic;



		/// <summary>
		/// DFS
		/// </summary>
		/// <param name="position"></param>
		/// <param name="fromNum"></param>
		/// <param name="from"></param>
		private static void DFS(long position , long fromNum, long from) {

			var num = fromNum + _countDic[position];
			_ansDic[position] = num;

			var nexts = _tree[position];

			foreach (var next in nexts) {
				if (next != from) {
					DFS(next, num, position);
				}
			}

		}


		/// <summary>
		/// スペースで区切られた文字列配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static string[] retreiveStringArray() {
			var inputArray = Console.ReadLine().Split(' ');
			return inputArray;
		}

		/// <summary>
		/// スペースで区切られた整数配列の入力を受け取る
		/// </summary>
		/// <returns></returns>
		private static long[] retreiveLongArray() {
			var inputArray = Console.ReadLine().Split(' ');
			var longArray = inputArray.Select(s => long.Parse(s));
			return longArray.ToArray();
		}


		/// <summary>
		/// 2組みずつの入力データ(数値)からTuppleListを作成する
		/// </summary>
		/// <param name="N"></param>
		/// <returns></returns>
		private static List<Tuple<long, long>> createLongTuppleList(long N) {
			var inpList = new List<Tuple<long, long>>();

			for (int i = 0; i < N; i++) {
				var inp = retreiveLongArray();
				var item1 = inp[0];
				var item2 = inp[1];
				inpList.Add(new Tuple<long, long>(item1, item2));
			}
			return inpList;
		}
	}
}