E. Vasya and a Tree
data structures; trees
Vasya has a tree consisting of \(n\) vertices with root in vertex \(1\). At first all vertices has \(0\) written on it.Let \(d(i, j)\) be the distance between vertices \(i\) and \(j\), i.e. number of edges in the shortest path from \(i\) to \(j\). Also, let's denote \(k\)-subtree of vertex \(x\) — set of vertices \(y\) such that next two conditions are met: \(x\) is the ancestor of \(y\) (each vertex is the ancestor of itself); \(d(x, y) \le k\). Vasya needs you to process \(m\) queries. The \(i\)-th query is a triple \(v_i\), \(d_i\) and \(x_i\). For each query Vasya adds value \(x_i\) to each vertex from \(d_i\)-subtree of \(v_i\).Report to Vasya all values, written on vertices of the tree after processing all queries.
The first line contains single integer \(n\) (\(1 \le n \le 3 \cdot 10^5\)) — number of vertices in the tree.Each of next \(n - 1\) lines contains two integers \(x\) and \(y\) (\(1 \le x, y \le n\)) — edge between vertices \(x\) and \(y\). It is guarantied that given graph is a tree.Next line contains single integer \(m\) (\(1 \le m \le 3 \cdot 10^5\)) — number of queries.Each of next \(m\) lines contains three integers \(v_i\), \(d_i\), \(x_i\) (\(1 \le v_i \le n\), \(0 \le d_i \le 10^9\), \(1 \le x_i \le 10^9\)) — description of the \(i\)-th query.
Print \(n\) integers. The \(i\)-th integers is the value, written in the \(i\)-th vertex after processing all queries.
In the first exapmle initial values in vertices are \(0, 0, 0, 0, 0\). After the first query values will be equal to \(1, 1, 1, 0, 0\). After the second query values will be equal to \(1, 11, 1, 0, 0\). After the third query values will be equal to \(1, 11, 1, 100, 0\).