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 maxpow = 40;
int BiggestPower(long long x) {
  int ans = 0;
  while (x > 1) {
    x = (x >> 1);
    ++ans;
  }
  return ans;
}
int main() {
  int n;
  cin >> n;
  long long k;
  cin >> k;
  int to[n];
  int w[n];
  for (int i = 0; i < n; ++i) {
    cin >> to[i];
  }
  for (int i = 0; i < n; ++i) {
    cin >> w[i];
  }
  int to_pow[n][maxpow];
  long long sum_w[n][maxpow];
  int min_w[n][maxpow];
  for (int i = 0; i < n; ++i) {
    to_pow[i][0] = to[i];
    sum_w[i][0] = w[i];
    min_w[i][0] = w[i];
  }
  for (int d = 1; d < maxpow; ++d) {
    for (int i = 0; i < n; i++) {
      to_pow[i][d] = to_pow[to_pow[i][d - 1]][d - 1];
      sum_w[i][d] = sum_w[i][d - 1] + sum_w[to_pow[i][d - 1]][d - 1];
      min_w[i][d] = min(min_w[i][d - 1], min_w[to_pow[i][d - 1]][d - 1]);
    }
  }
  int to_pow_ans[n];
  long long sum_w_ans[n];
  int min_w_ans[n];
  for (int i = 0; i < n; i++) {
    to_pow_ans[i] = i;
    sum_w_ans[i] = 0;
    min_w_ans[i] = 1e+9;
  }
  while (k > 0) {
    int d = BiggestPower(k);
    long long p = 1;
    p = (p << d);
    k -= p;
    for (int i = 0; i < n; i++) {
      sum_w_ans[i] += sum_w[to_pow_ans[i]][d];
      min_w_ans[i] = min(min_w_ans[i], min_w[to_pow_ans[i]][d]);
      to_pow_ans[i] = to_pow[to_pow_ans[i]][d];
    }
  }
  for (int i = 0; i < n; i++) {
    cout << sum_w_ans[i] << " " << min_w_ans[i] << endl;
  }
  cout << endl;
}