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 fa[100010][35], Min[100010][35];
long long w[100010][35], n, k;
long long Sum(int x, long long p) {
  if (p == 0) return 0;
  int t = 0;
  long long sum = 1;
  while (sum <= p) {
    t++;
    sum <<= 1;
  }
  t--;
  sum >>= 1;
  return w[x][t] + Sum(fa[x][t], p - sum);
}
int Minn(int x, long long p) {
  if (p == 0) return 1e9;
  int t = 0;
  long long sum = 1;
  while (sum <= p) {
    t++;
    sum <<= 1;
  }
  t--;
  sum >>= 1;
  return min(Min[x][t], Minn(fa[x][t], p - sum));
}
int main() {
  scanf("%I64d%I64d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%d", &fa[i][0]);
  for (int i = 0; i < n; i++) scanf("%I64d", &w[i][0]), Min[i][0] = w[i][0];
  for (int i = 1; i <= 34; i++)
    for (int j = 0; j < n; j++) fa[j][i] = fa[fa[j][i - 1]][i - 1];
  for (int i = 1; i <= 34; i++)
    for (int j = 0; j < n; j++) w[j][i] = w[j][i - 1] + w[fa[j][i - 1]][i - 1];
  for (int i = 1; i <= 34; i++)
    for (int j = 0; j < n; j++)
      Min[j][i] = min(Min[j][i - 1], Min[fa[j][i - 1]][i - 1]);
  for (int i = 0; i < n; i++) printf("%I64d %d\n", Sum(i, k), Minn(i, k));
}