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 Son[100010][50];
long long Ans[100010][50];
int Min[100010][50];
long long Solve1(int Cur, long long k) {
  if (k == 0) return 0;
  int xx = 0;
  long long x = 1;
  while (x <= k) xx++, x <<= 1;
  xx--;
  x >>= 1;
  return Ans[Cur][xx] + Solve1(Son[Cur][xx], k - x);
}
int Solve2(int Cur, long long k) {
  if (k == 0) return 2147483647;
  int xx = 0;
  long long x = 1;
  while (x <= k) xx++, x <<= 1;
  xx--;
  x >>= 1;
  return min(Min[Cur][xx], Solve2(Son[Cur][xx], k - x));
}
int main() {
  int n;
  long long k;
  scanf("%d %I64d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%d", &Son[i][0]);
  for (int i = 0; i < n; i++) scanf("%I64d", &Ans[i][0]), Min[i][0] = Ans[i][0];
  for (int t = 1; t <= 40; t++)
    for (int i = 0; i < n; i++) Son[i][t] = Son[Son[i][t - 1]][t - 1];
  for (int t = 1; t <= 40; t++)
    for (int i = 0; i < n; i++)
      Ans[i][t] = Ans[i][t - 1] + Ans[Son[i][t - 1]][t - 1];
  for (int t = 1; t <= 40; t++)
    for (int i = 0; i < n; i++)
      Min[i][t] = min(Min[i][t - 1], Min[Son[i][t - 1]][t - 1]);
  for (int i = 0; i < n; i++) printf("%I64d %d\n", Solve1(i, k), Solve2(i, k));
}