You are given a functional graph. It is a directed graph, in which from each vertex goes exactly one arc. The vertices are numerated from 0 to n - 1. Graph is given as the array f0, f1, ..., fn - 1, where fi -- the number of vertex to which goes the only arc from the vertex i. Besides you are given array with weights of the arcs w0, w1, ..., wn - 1, where wi -- the arc weight from i to fi. Also you are given the integer k (the length of the path) and you need to find for each vertex two numbers si and mi, where: The length of the path is the number of arcs on this path. The first line contains two integers n, k (1 ≤ n ≤ 105, 1 ≤ k ≤ 1010). The second line contains the sequence f0, f1, ..., fn - 1 (0 ≤ fi < n) and the third -- the sequence w0, w1, ..., wn - 1 (0 ≤ wi ≤ 108). Print n lines, the pair of integers si, mi in each line.