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 INF = 1000000009;
const long long INFL = 1e18 + 5LL;
const long double EPS = 1e-11;
const long long MOD = 998244353;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  long long n, k;
  cin >> n >> k;
  vector<long long> f(n), w(n);
  for (int i = 0; i < n; ++i) {
    cin >> f[i];
  }
  for (int i = 0; i < n; ++i) {
    cin >> w[i];
  }
  vector<long long> s(w), m(w), v(f);
  for (int di = 44; di >= 0; --di) {
    if ((k >> di) < 2LL) {
      continue;
    }
    vector<long long> ns(s), nm(m), nv(v);
    for (int i = 0; i < n; ++i) {
      ns[i] += s[v[i]];
      nm[i] = min(nm[i], m[v[i]]);
      nv[i] = v[v[i]];
    }
    if ((k >> di) & 1) {
      for (int i = 0; i < n; ++i) {
        ns[i] += w[nv[i]];
        nm[i] = min(nm[i], w[nv[i]]);
        nv[i] = f[nv[i]];
      }
    }
    s = ns;
    m = nm;
    v = nv;
  }
  for (int i = 0; i < n; ++i) {
    cout << s[i] << " " << m[i] << "\n";
  }
  return 0;
}