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 MAXN = 1e5 + 10;
const int LOGMAXN = 40;
const int INF = 1e9;
int f[MAXN];
int c[MAXN];
long long s[MAXN][LOGMAXN];
long long mn[MAXN][LOGMAXN];
int p[MAXN][LOGMAXN];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, k;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> f[i];
  for (int i = 0; i < n; i++) cin >> c[i];
  for (int i = 0; i < n; i++) p[i][1] = f[i], s[i][1] = mn[i][1] = c[i];
  for (int i = 2; i <= LOGMAXN; i++)
    for (int j = 0; j < n; j++) {
      p[j][i] = p[p[j][i - 1]][i - 1];
      s[j][i] = s[j][i - 1] + s[p[j][i - 1]][i - 1];
      mn[j][i] = min(mn[j][i - 1], mn[p[j][i - 1]][i - 1]);
    }
  for (int i = 0; i < n; i++) {
    int x = i;
    long long m1 = INF, s1 = 0LL;
    for (int j = LOGMAXN - 1; j >= 0; j--)
      if ((1LL << j) & k) {
        j++;
        s1 += 1LL * s[x][j];
        m1 = min(m1, mn[x][j]);
        x = p[x][j];
        j--;
      }
    cout << s1 << " " << m1 << endl;
  }
  return 0;
}