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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;
import java.util.ArrayList;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author silviase
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DKi solver = new DKi();
        solver.solve(1, in, out);
        out.close();
    }

    static class DKi {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int q = in.nextInt();
            Graph g = new Graph(n);
            for (int i = 0; i < n - 1; i++) {
                g.addUnDirectedEdge(in.nextInt() - 1, in.nextInt() - 1);
            }
            for (int i = 0; i < q; i++) {
                g.addCost(in.nextInt() - 1, in.nextInt());
            }

            // 0から順にdfsをする.
            g.dfs(0, g.getCost(0));

            for (int i = 0; i < n; i++) {
                out.println(g.getCost(i));
            }

        }

    }

    static class Graph {
        private int n;
        private ArrayList<Integer>[] adj;
        private int[] cost;
        private boolean[] visited;

        public Graph(int size) {
            n = size;
            cost = new int[n];
            visited = new boolean[n];
            Arrays.fill(visited, false);
            adj = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                adj[i] = new ArrayList<>();
            }
        }

        public void addEdge(int from, int to) {
            adj[from].add(to);
        }

        public void addUnDirectedEdge(int from, int to) {
            addEdge(from, to);
            addEdge(to, from);
        }

        public void addCost(int index, int value) {
            cost[index] += value;
        }

        public void dfs(int index, int cost) {
            if (visited[index]) {
                return;
            }
            visited[index] = true;
            this.cost[index] = cost;
            ArrayList<Integer> nxtAl = adj[index];
            for (int nxt : nxtAl) {
                dfs(nxt, cost + getCost(nxt));
            }
        }

        public int getCost(int i) {
            return cost[i];
        }

    }
}