B'You are given a rooted tree on n vertices, its root is the vertex number 1 . The i -th vertex contains a number w_i . Split it into the minimum possible number of vertical paths in such a way that each path contains no more than L vertices and the sum of integers w_i on each path does not exceed S . Each vertex should belong to exactly one path. A vertical path is a sequence of vertices v_1, v_2, ldots, v_k where v_i ( i ge 2 ) is the parent of v_{i - 1} . The first line contains three integers n , L , S ( 1 <= n <= 10^5 , 1 <= L <= 10^5 , 1 <= S <= 10^{18} ) -- the number of vertices, the maximum number of vertices in one path and the maximum sum in one path. The second line contains n integers w_1, w_2, ldots, w_n ( 1 <= w_i <= 10^9 ) -- the numbers in the vertices of the tree. The third line contains n - 1 integers p_2, ldots, p_n ( 1 <= p_i < i ), where p_i is the parent of the i -th vertex in the tree. Output one number -- the minimum number of vertical paths. If it is impossible to split the tree, output -1 . In the first sample the tree is split into {1 }, {2 }, {3 } . In the second sample the tree is split into {1, 2 }, {3 } or {1, 3 }, {2 } . In the third sample it is impossible to split the tree. '...