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 main() {
  int n;
  long long k;
  scanf("%d %I64d", &n, &k);
  int f[n];
  long long w[n];
  for (int i = 0; i < n; i++) scanf("%d", &f[i]);
  for (int i = 0; i < n; i++) scanf("%I64d", &w[i]);
  int anc[n][34];
  long long sum[n][34], mn[n][34];
  for (int i = 0; i < n; i++) {
    anc[i][0] = f[i];
    sum[i][0] = w[i];
    mn[i][0] = w[i];
  }
  for (int i = 1; i < 34; i++) {
    for (int j = 0; j < n; j++) {
      anc[j][i] = anc[anc[j][i - 1]][i - 1];
      sum[j][i] = sum[anc[j][i - 1]][i - 1] + sum[j][i - 1];
      mn[j][i] = min(mn[anc[j][i - 1]][i - 1], mn[j][i - 1]);
    }
  }
  for (int i = 0; i < n; i++) {
    int ank = i;
    long long csum = 0, cmn = 1001001001;
    for (long long j = 34; j >= 0; j--) {
      if (k & (1ll << j)) {
        csum += sum[ank][j];
        cmn = min(cmn, mn[ank][j]);
        ank = anc[ank][j];
      }
    }
    printf("%I64d %I64d\n", csum, cmn);
  }
  return 0;
}