702_E. 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.

<image> 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

Example input:
5 3
1 2 3 4 0
4 1 2 14 3

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

4 4
0 1 2 3
0 1 2 3


Example output:
                                                               7                                                                1
                                                              17                                                                1
                                                              19                                                                2
                                                              21                                                                3
                                                               8                                                                1

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

                                                               0                                                                0
                                                               4                                                                1
                                                               8                                                                2
                                                              12                                                                3


Tags: data structures
graphs
Difficulty rating: 2100

Solution:
#include <bits/stdc++.h>
using namespace std;
int f[120000][40], h[120000][40], i, j, k, n, x, t;
long long m, s, g[120000][40];
int main() {
  scanf("%d%I64d", &n, &m);
  for (i = 1; i <= n; i++) scanf("%d", &x), f[i][0] = ++x;
  for (i = 1; i <= n; i++) scanf("%d", &x), g[i][0] = h[i][0] = x;
  for (i = 1; (1LL << i) <= m; i++)
    for (j = 1; j <= n; j++) {
      f[j][i] = f[f[j][i - 1]][i - 1];
      g[j][i] = g[j][i - 1] + g[f[j][i - 1]][i - 1];
      h[j][i] = min(h[j][i - 1], h[f[j][i - 1]][i - 1]);
    }
  for (i = 1; i <= n; i++) {
    k = i, s = 0, t = h[i][0];
    for (j = 0; (1LL << j) <= m; j++)
      if ((1LL << j) & m) s += g[k][j], t = min(t, h[k][j]), k = f[k][j];
    printf("%I64d %d\n", s, t);
  }
}