E. Analysis of Pathes in Functional Graph
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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.

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 si and mi, where:

• si — the sum of the weights of all arcs of the path with length equals to k which starts from the vertex i;
• mi — 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, ..., fn - 1 (0 ≤ fi < n) and the third — the sequence w0, w1, ..., wn - 1 (0 ≤ wi ≤ 108).

Output

Print n lines, the pair of integers si, mi in each line.

Examples
Input
7 31 2 3 4 3 2 66 3 1 4 2 2 3
Output
10 18 17 110 28 27 19 3
Input
4 40 1 2 30 1 2 3
Output
0 04 18 212 3
Input
5 31 2 3 4 04 1 2 14 3
Output
7 117 119 221 38 1