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 double eps = 1e-10, pi = acos(-1.0);
long long n, N = 40, k;
long long nxt[40][100005], sum[40][100005], mi[40][100005];
void query(long long node, long long dis) {
  long long x = 0, y = LLONG_MAX;
  for (int i = 0; i < N; i++)
    if (dis & (1LL << i)) {
      x += (sum[i][node]);
      y = min(y, mi[i][node]);
      node = nxt[i][node];
    }
  cout << x << ' ' << y << "\n";
}
int main() {
  long long n, k;
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) {
    cin >> nxt[0][i];
    nxt[0][i]++;
  }
  for (long long i = 1; i <= n; i++) {
    cin >> sum[0][i];
    mi[0][i] = sum[0][i];
  }
  for (int i = 1; i < N; i++)
    for (int j = 1; j <= n; j++) {
      nxt[i][j] = nxt[i - 1][nxt[i - 1][j]];
      sum[i][j] = sum[i - 1][nxt[i - 1][j]] + sum[i - 1][j];
      mi[i][j] = min(mi[i - 1][nxt[i - 1][j]], mi[i - 1][j]);
    }
  for (int i = 1; i <= n; i++) query(i, k);
  return 0;
}