B'You are given a rooted tree. It contains n vertices, which are numbered from 1 to n . The root is the vertex 1 . Each edge has two positive integer values. Thus, two positive integers a_j and b_j are given for each edge. Output n-1 numbers r_2, r_3, ... , r_n , where r_i is defined as follows. Consider the path from the root (vertex 1 ) to i ( 2 <= i <= n ). Let the sum of the costs of a_j along this path be A_i . Then r_i is equal to the length of the maximum prefix of this path such that the sum of b_j along this prefix does not exceed A_i . Consider an example. In this case: The first line contains an integer t ( 1 <= t <= 10^4 ) -- the number of test cases in the test. The descriptions of test cases follow. Each description begins with a line that contains an integer n ( 2 <= n <= 2 cdot10^5 ) -- the number of vertices in the tree. This is followed by n-1 string, each of which contains three numbers p_j, a_j, b_j ( 1 <= p_j <= n ; 1 <= a_j,b_j <= 10^9 ) -- the ancestor of the vertex j , the first and second values an edge that leads from p_j to j . The value of j runs through all values from 2 to n inclusive. It is guaranteed that each set of input data has a correct hanged tree with a root at the vertex 1 . It is guaranteed that the sum of n over all input test cases does not exceed 2 cdot10^5 . For each test case, output n-1 integer in one line: r_2, r_3, ... , r_n . The first example is clarified in the statement. In the second example: '...