Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 9;
long long n, k;
long long p[N], q[N], sparce_table[N][40], min_[N][40], ans[N][40];
int main() {
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> p[i];
  for (int i = 0; i < n; i++) cin >> q[i];
  for (int i = 0; i < n; i++) {
    sparce_table[i][0] = p[i];
    ans[i][0] = min_[i][0] = q[i];
  }
  for (int i = 1; i < 40; i++) {
    for (int j = 0; j < n; j++) {
      sparce_table[j][i] = sparce_table[sparce_table[j][i - 1]][i - 1];
      ans[j][i] = ans[j][i - 1] + ans[sparce_table[j][i - 1]][i - 1];
      min_[j][i] = min(min_[j][i - 1], min_[sparce_table[j][i - 1]][i - 1]);
    }
  }
  for (int i = 0; i < n; i++) {
    int index = i;
    long long counter = 0;
    long long big = 1e18;
    long long rem = k;
    for (int ii = 39; ii >= 0; ii--) {
      if ((1ll << ii) <= rem) {
        rem -= (1ll << ii);
        counter += ans[index][ii];
        big = min(big, min_[index][ii]);
        index = sparce_table[index][ii];
      }
    }
    cout << counter << " " << big << endl;
  }
}