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;
using ll = long long;
using P = pair<int, int>;
template <class T>
void chmin(T &a, const T &b) noexcept {
  if (b < a) a = b;
}
template <class T>
void chmax(T &a, const T &b) noexcept {
  if (a < b) a = b;
}
void debug_out() { cout << "\n"; }
template <class T, class... Args>
void debug_out(const T &x, const Args &...args) {
  cout << x << " ";
  debug_out(args...);
}
int main() {
  std::cin.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  std::cout << std::fixed << std::setprecision(15);
  ll n, m;
  cin >> n >> m;
  vector<int> a(n);
  int k = 1;
  while ((1LL << k) <= m) k++;
  vector<vector<int> > par(k, vector<int>(n, -1));
  vector<vector<ll> > sum_w(k, vector<ll>(n, 0));
  vector<vector<ll> > min_w(k, vector<ll>(n, 1LL << 60));
  for (int i = 0; i < (n); ++i) {
    cin >> par[0][i];
  }
  for (int i = 0; i < (n); ++i) {
    cin >> sum_w[0][i];
    min_w[0][i] = sum_w[0][i];
  }
  for (int i = 0; i < (k - 1); ++i)
    for (int v = 0; v < (n); ++v) {
      if (par[i][v] < 0)
        par[i + 1][v] = -1;
      else {
        par[i + 1][v] = par[i][par[i][v]];
        sum_w[i + 1][v] = sum_w[i][v] + sum_w[i][par[i][v]];
        min_w[i + 1][v] = min(min_w[i][v], min_w[i][par[i][v]]);
      }
    }
  for (int i = 0; i < (n); ++i) {
    int ind = i;
    int tk = k - 1;
    ll cur = 0;
    ll s = 0, mini = 1LL << 60;
    while (tk >= 0) {
      if (cur == m) break;
      if (cur + (1LL << tk) <= m) {
        s += sum_w[tk][ind];
        chmin(mini, min_w[tk][ind]);
        ind = par[tk][ind];
        cur += 1LL << tk;
      }
      tk--;
    }
    cout << s << " " << mini << "\n";
  }
  return 0;
}