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 MAX = 100005;
const int LOG = 34;
long long weight[MAX][LOG], mn[MAX][LOG], dp[MAX][LOG];
long long w[MAX], f[MAX];
pair<long long, long long> query(int x, long long k) {
  pair<long long, long long> ans(0, LLONG_MAX);
  for (int i = LOG - 1; i >= 0; --i) {
    if ((k >> i) & 1ll) {
      ans.first += weight[x][i];
      ans.second = min(ans.second, mn[x][i]);
      x = dp[x][i];
    }
  }
  return ans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  long long k;
  int n;
  cin >> n >> k;
  for (int i = 0; i < n; ++i) cin >> f[i];
  for (int i = 0; i < n; ++i) cin >> w[i];
  for (int i = 0; i < n; ++i) {
    weight[i][0] = w[i];
    mn[i][0] = w[i];
    dp[i][0] = f[i];
  }
  for (int j = 0; j < LOG - 1; ++j) {
    for (int i = 0; i < n; ++i) {
      dp[i][j + 1] = dp[dp[i][j]][j];
      weight[i][j + 1] = weight[i][j] + weight[dp[i][j]][j];
      mn[i][j + 1] = min(mn[i][j], mn[dp[i][j]][j]);
    }
  }
  for (int i = 0; i < n; ++i) {
    pair<long long, long long> ans = query(i, k);
    cout << ans.first << ' ' << ans.second << '\n';
  }
}