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 long long oo = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-9;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n, k;
  cin >> n >> k;
  long long K = 34;
  vector<vector<long long> > f(K, vector<long long>(n)),
      wsum(K, vector<long long>(n)), wmin(K, vector<long long>(n));
  for (long long i = (0); i < (n); i++) cin >> f[0][i];
  for (long long i = (0); i < (n); i++)
    cin >> wsum[0][i], wmin[0][i] = wsum[0][i];
  for (long long d = (0); d < (K - 1); d++)
    for (long long i = (0); i < (n); i++) {
      f[d + 1][i] = f[d][f[d][i]];
      wmin[d + 1][i] = min(wmin[d][i], wmin[d][f[d][i]]);
      wsum[d + 1][i] = wsum[d][i] + wsum[d][f[d][i]];
    }
  for (long long i = (0); i < (n); i++) {
    long long csum = 0, cmin = INT_MAX, j = i;
    for (long long d = (0); d < (K); d++)
      if (k & (1LL << d)) {
        csum += wsum[d][j];
        cmin = min(cmin, wmin[d][j]);
        j = f[d][j];
      }
    cout << csum << " " << cmin << "\n";
  }
}