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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Scanner;
class Main{


	static final int MOD = 1000000007;

	static	ArrayList<TreeNode> tree;
	static HashSet<Integer> set;
	static int[] ans;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);			//文字の入力
		int n = sc.nextInt();
		int q = sc.nextInt();
		tree = new ArrayList<TreeNode>();
		
//		for(int i = 0;i < n;i++){
//			TreeNode node = new TreeNode(i, 0);
//			tree.add(node);
//		}
		
		for(int i = 0;i < n-1;i++){
			int a = sc.nextInt()-1;
			int b = sc.nextInt()-1;
//			tree.get(a).childlen.add(tree.get(b));			//子ノードの追加
//			tree.get(b).childlen.add(tree.get(a));			//子ノードの追加

		}

		for(int i = 0;i < q;i++){
			int p = sc.nextInt()-1;
			int x = sc.nextInt();
//			tree.get(p).sum += x;
		}
		int counter = 0;
		
		ans = new int[n];
		set = new HashSet<Integer>();
		set.add(0);
	//	dfs(0, 0);
		
		
		
		for(int i = 0;i < n;i++){
			System.out.println(ans[i]);
		}





	}

	static void dfs(int current,int num){

		ans[current] = num + tree.get(current).sum;
		set.add(current);
		for(TreeNode child:tree.get(current).childlen ){
			if(ans[child.value]== 0){
				dfs(child.value, num +tree.get(current).sum);
			}
		}

	}





	static int upperbond(int k,int min,int[] data){		//kより小さい最大の値をdataの中から探し、返す二分探索
		int max = data.length;
		//		if(min == data.length-1){
		//			if(data[min] > k){
		//				return min;
		//			}
		//		}

		while(max-min > 1){
			int mid = (max+min)/2;
			if(data[mid] >= k){
				max = mid;
			}else{
				min = mid;
			}
		}

		return max;
	}

	static int lowerbond(int k,int min,int[] data){		//kより大きい最小の値をdataの中から探し、返す二分探索
		int max = data.length;

		while(max-min > 1){
			int mid = (max+min)/2;
			if(data[mid] >= k){
				max = mid;
			}else{
				min = mid;
			}
		}
		return min;
	}



	static int gcd(int a,int b){				//最大公約数を返す
		if(b == 0){
			return a;
		}else{
			return gcd(b, a%b);
		}
	}
	static long gcd(long a,long b){
		if(b == 0){
			return a;
		}else{
			return gcd(b, a%b);
		}
	}



	static long lcm (long a, long b) {
		long g = gcd(a,b);
		return a/g*b;
	}




}

class TreeNode{
	int value;
	int sum;
	ArrayList<TreeNode> childlen;

	public TreeNode(int v,int s) {
		this.value = v;
		this.sum = s;
		this.childlen = new ArrayList<TreeNode>();
	}


}


class Edge  implements Comparable{

	int index;
	HashSet<Integer> hen;
	HashSet<Integer> used;
	HashMap<Integer, Integer> map;
	int size;


	public Edge(int index) {
		// TODO 自動生成されたコンストラクター・スタブ
		this.index = index;
		hen = new HashSet();
		used = new HashSet<Integer>();
		map = new HashMap<Integer,Integer>();
	}

	public int compareTo(Object other) {
		Edge otherpair = (Edge)other;

		return   otherpair.hen.size() - hen.size();
	}
}

class Food implements Comparable{

	int minits;
	int score;
	double cospa;

	public Food(int from,int end,double c) {
		this.minits = from;
		this.score = end;
		this.cospa = c;
		// TODO 自動生成されたコンストラクター・スタブ
	}

	@Override
	public int compareTo(Object other) {
		Food otherpair = (Food)other;
		int dif = Double.compare(otherpair.cospa, cospa);
		return   dif;
	}

}

class Pair implements Comparable{
	int from;
	int end;
	public Pair(int from,int end) {
		this.from = from;
		this.end = end;
		// TODO 自動生成されたコンストラクター・スタブ
	}

	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return  from - otherpair.from;
	}








}