#D11259. Analysis of Pathes in Functional Graph
Analysis of Pathes in Functional Graph
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 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 3 1 2 3 4 3 2 6 6 3 1 4 2 2 3
Output
10 1 8 1 7 1 10 2 8 2 7 1 9 3
Input
4 4 0 1 2 3 0 1 2 3
Output
0 0 4 1 8 2 12 3
Input
5 3 1 2 3 4 0 4 1 2 14 3
Output
7 1 17 1 19 2 21 3 8 1
inputFormat
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).
outputFormat
Output
Print n lines, the pair of integers si, mi in each line.
Examples
Input
7 3 1 2 3 4 3 2 6 6 3 1 4 2 2 3
Output
10 1 8 1 7 1 10 2 8 2 7 1 9 3
Input
4 4 0 1 2 3 0 1 2 3
Output
0 0 4 1 8 2 12 3
Input
5 3 1 2 3 4 0 4 1 2 14 3
Output
7 1 17 1 19 2 21 3 8 1
样例
5 3
1 2 3 4 0
4 1 2 14 3
7 1
17 1
19 2
21 3
8 1