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 wnext[34 + 1][(int)1e5 + 1];
int64_t wsum[34 + 1][(int)1e5 + 1];
int64_t wmin[34 + 1][(int)1e5 + 1];
int main() {
  int n;
  int64_t k;
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    cin >> wnext[0][i];
    wnext[0][i] += 1;
  }
  for (int i = 1; i <= n; ++i) {
    cin >> wsum[0][i];
    wmin[0][i] = wsum[0][i];
  }
  for (int l = 1; l <= 34; ++l) {
    for (int i = 1; i <= n; ++i) {
      int mid = wnext[l - 1][i];
      wnext[l][i] = wnext[l - 1][mid];
      wsum[l][i] = wsum[l - 1][i] + wsum[l - 1][mid];
      wmin[l][i] = min(wmin[l - 1][i], wmin[l - 1][mid]);
    }
  }
  for (int i = 1; i <= n; ++i) {
    int pos = i;
    int64_t ws = wsum[0][pos], wm = wmin[0][pos];
    pos = wnext[0][pos];
    int64_t left = k - 1;
    while (left) {
      for (int l = 34; l >= 0; --l) {
        if ((1ll << l) <= left) {
          ws += wsum[l][pos];
          wm = min(wm, wmin[l][pos]);
          pos = wnext[l][pos];
          left -= (1ll << l);
          break;
        }
      }
    }
    cout << ws << " " << wm << "\n";
  }
}