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 LG = 40;
const int N = 1e5 + 5;
const int W = 1e8 + 5;
int n, par[N][LG], mn[N][LG];
long long k, sum[N][LG];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(NULL);
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> par[i][0];
  }
  for (int i = 0; i < n; i++) {
    cin >> sum[i][0];
    mn[i][0] = sum[i][0];
  }
  for (int j = 1; 1LL << j <= k; j++) {
    for (int i = 0; i < n; i++) {
      par[i][j] = par[par[i][j - 1]][j - 1];
      sum[i][j] = sum[i][j - 1] + sum[par[i][j - 1]][j - 1];
      mn[i][j] = min(mn[i][j - 1], mn[par[i][j - 1]][j - 1]);
    }
  }
  for (int i = 0; i < n; i++) {
    int v = i, m = W;
    long long s = 0, x = k;
    int j = 0;
    while (x) {
      if (x & 1) {
        s += sum[v][j];
        m = min(m, mn[v][j]);
        v = par[v][j];
      }
      j++;
      x >>= 1;
    }
    cout << s << ' ' << m << '\n';
  }
  return 0;
}