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;
template <typename T>
using Matrix = vector<vector<T>>;
template <typename T>
Matrix<T> matrix(int R, int C, T x = T()) {
  return Matrix<T>(R, vector<T>(C, x));
}
struct S {
  ll sum;
  int min;
};
S operator+(S a, S b) { return {a.sum + b.sum, min(a.min, b.min)}; }
S& operator+=(S& a, S b) { return a = a + b; }
struct SparseTable {
  Matrix<int> images;
  Matrix<S> data;
  SparseTable(int n, int maxjump, vector<int> direct_images,
              vector<int> weights) {
    images = matrix<int>(maxjump + 1, n);
    images[0] = direct_images;
    data = matrix<S>(maxjump + 1, n);
    for (auto i = 0; i < n; i++) data[0][i] = {weights[i], weights[i]};
    for (auto k = 1; k <= maxjump; k++)
      for (auto i = 0; i < n; i++) {
        images[k][i] = images[k - 1][images[k - 1][i]];
        data[k][i] = data[k - 1][i] + data[k - 1][images[k - 1][i]];
      }
  }
  S query(int n, ll k) {
    auto result = S{0LL, numeric_limits<int>::max()};
    for (auto i = 0; k > 0; i++)
      if (k & 1LL << i) {
        result += data[i][n];
        n = images[i][n];
        k -= 1LL << i;
      }
    return result;
  }
};
int main() {
  int n;
  ll k;
  scanf("%d %lld", &n, &k);
  auto images = vector<int>(n);
  for (auto& x : images) scanf("%d", &x);
  auto weights = vector<int>(n);
  for (auto& x : weights) scanf("%d", &x);
  auto table = SparseTable(n, 40, images, weights);
  for (auto i = 0; i < n; i++) {
    auto answer = table.query(i, k);
    printf("%lld %d\n", answer.sum, answer.min);
  }
}