A10522. Analysis of Pathes in Functional Graph

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 $f_{0},f_{1},\dots,f_{n-1}$, 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 $w_{0},w_{1},\dots,w_{n-1}$, where $w_{i}$ — the arc weight from $i$ to $f_{i}$.


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.

The first line contains two integers $n,k \ ( 1\le n
\le10^{5},1\le k\le10^{10})$. The second line contains the sequence $f_{0},f_{1},\dots,f_{n-1}\ ( 0\le f_{i}<n )$ and the third — the sequence $w_{0},w_{1},...,w_{n-1}\ ( 0\le w_{i}\le10^{8} )$.

Print $n$ lines, the pair of integers $s_{i},m_{i}$ in each line.