#P702E. Analysis of Pathes in Functional Graph

    ID: 3609 Type: RemoteJudge 2000ms 512MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>data structuresgraphs*2100

Analysis of Pathes in Functional Graph

No submission language available for this problem.

Description

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.

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.

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.

Samples

7 3
1 2 3 4 3 2 6
6 3 1 4 2 2 3

10 1
8 1
7 1
10 2
8 2
7 1
9 3

4 4
0 1 2 3
0 1 2 3

0 0
4 1
8 2
12 3

5 3
1 2 3 4 0
4 1 2 14 3

7 1
17 1
19 2
21 3
8 1