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;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long n, k;
  cin >> n >> k;
  vector<vector<long long> > hopp(40, vector<long long>(n)),
      wsum(40, vector<long long>(n)), minw(40, vector<long long>(n));
  for (auto &x : hopp[0]) cin >> x;
  for (auto &x : wsum[0]) cin >> x;
  for (int i = (0); i < int(n); ++i) minw[0][i] = wsum[0][i];
  for (int i = (1); i < int(40); ++i)
    for (int j = (0); j < int(n); ++j) hopp[i][j] = hopp[i - 1][hopp[i - 1][j]];
  for (int i = (1); i < int(40); ++i)
    for (int j = (0); j < int(n); ++j)
      wsum[i][j] = wsum[i - 1][j] + wsum[i - 1][hopp[i - 1][j]];
  for (int i = (1); i < int(40); ++i)
    for (int j = (0); j < int(n); ++j)
      minw[i][j] = min(minw[i - 1][j], minw[i - 1][hopp[i - 1][j]]);
  auto sum = [&](int v, long long l) {
    long long res = 0;
    int i = 0;
    while (l) {
      if (l & 1) {
        res += wsum[i][v];
        v = hopp[i][v];
      }
      l /= 2;
      i++;
    }
    return res;
  };
  auto mn = [&](int v, long long l) {
    long long res = 1e9;
    int i = 0;
    while (l) {
      if (l & 1) {
        res = min(res, minw[i][v]);
        v = hopp[i][v];
      }
      l /= 2;
      i++;
    }
    return res;
  };
  for (int i = (0); i < int(n); ++i)
    cout << sum(i, k) << ' ' << mn(i, k) << endl;
}