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 int N = 1e5 + 5;
int n;
long long k;
int w[N], f[N], cur[N], anw[N], tw[N], tf[N];
long long s[N], ans[N], ts[N];
int main() {
  scanf("%d%I64d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%d", f + i), cur[i] = i;
  for (int i = 0; i < n; i++) {
    scanf("%d", w + i);
    anw[i] = 1e9 + 7;
    s[i] = w[i];
    ans[i] = 0;
  }
  for (long long mask = 1; mask <= k; mask <<= 1) {
    if (mask & k) {
      for (int i = 0; i < n; i++) {
        ans[i] += s[cur[i]];
        anw[i] = min(anw[i], w[cur[i]]);
        cur[i] = f[cur[i]];
      }
    }
    for (int i = 0; i < n; i++) {
      tw[i] = min(w[i], w[f[i]]);
      ts[i] = s[i] + s[f[i]];
      tf[i] = f[f[i]];
    }
    for (int i = 0; i < n; i++) {
      w[i] = tw[i];
      s[i] = ts[i];
      f[i] = tf[i];
    }
  }
  for (int i = 0; i < n; i++) {
    printf("%I64d %d\n", ans[i], anw[i]);
  }
  return 0;
}