Ki

Problem Statement

Ki Problem Description Given is a rooted tree with N vertices numbered 1 to N . The root is Vertex 1, and the i -th edge ( 1 ≤ i ≤ 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 ≤ j ≤ 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 ≤ N ≤ 2 × 10^5 1 ≤ Q ≤ 2 × 10^5 1 ≤ a_i 1 ≤ p_j ≤ N 1 ≤ x_j ≤ 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, ..., N after all operations, in this order, with spaces in between. Examples Example 1: Input: 4 3 1 2 2 3 2 4 2 10 1 100 3 1 Output: 100 110 111 110 Explanation: The tree i