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;
int mmin[100010][50];
long long sum[100010][50];
int son[100010][50];
long long poww[50];
void pre() {
  poww[0] = 1;
  for (int i = 1; i <= 40; i++) poww[i] = poww[i - 1] << 1;
}
long long n, k;
long long SUM;
int MMIN;
void solve(int h, long long k) {
  SUM = 0, MMIN = 0;
  MMIN = 2e9;
  for (int i = 40; i >= 0; i--)
    if (poww[i] <= k)
      MMIN = min(MMIN, mmin[h][i]), SUM += sum[h][i], k -= poww[i],
      h = son[h][i];
}
long long read() {
  long long sum = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') ch = getchar();
  while (ch <= '9' && ch >= '0') sum = sum * 10 + ch - '0', ch = getchar();
  return sum;
}
int main() {
  pre();
  n = read(), k = read();
  for (int i = 0; i < n; i++) son[i][0] = read();
  for (int i = 0; i < n; i++) mmin[i][0] = sum[i][0] = read();
  for (int i = 1; i <= 40; i++)
    for (int j = 0; j < n; j++) {
      son[j][i] = son[son[j][i - 1]][i - 1];
      sum[j][i] = sum[son[j][i - 1]][i - 1] + sum[j][i - 1];
      mmin[j][i] = min(mmin[j][i - 1], mmin[son[j][i - 1]][i - 1]);
    }
  for (int i = 0; i < n; i++) {
    solve(i, k);
    cout << SUM << " " << MMIN << '\n';
  }
  return 0;
}