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, ..., f_n - 1, where f_i — 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, ..., w_n - 1, where w_i — the arc weight from i to f_i.

$\text{[math]}$ The graph from the first sample test.

Also you are given the integer k (the length of the path) and you need to find for each vertex two numbers s_i and m_i, where:

s_i — the sum of the weights of all arcs of the path with length equals to k which starts from the vertex i;
m_i — the minimal weight from all arcs on the path with length k which starts from the vertex i.

The length of the path is the number of arcs on this path.

Input

The first line contains two integers n, k (1 ≤ n ≤ 10⁵, 1 ≤ k ≤ 10¹⁰). The second line contains the sequence f₀, f₁, ..., f_n - 1 (0 ≤ f_i < n) and the third — the sequence w₀, w₁, ..., w_n - 1 (0 ≤ w_i ≤ 10⁸).

Output

Print n lines, the pair of integers s_i, m_i in each line.

Analysis of Pathes in Functional Graph

Examples