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 + 100;
long long s[N][40], m[N][40], a1, a2;
int p[N][40];
int n;
bitset<40> k;
int main() {
  scanf("%d%I64d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%d", &p[i][0]);
  for (int i = 0; i < n; i++) {
    scanf("%I64d", &m[i][0]);
    s[i][0] = m[i][0];
  }
  for (int _ = 0; _ < 39; _++)
    for (int i = 0; i < n; i++) {
      p[i][_ + 1] = p[p[i][_]][_];
      s[i][_ + 1] = s[i][_] + s[p[i][_]][_];
      m[i][_ + 1] = (m[i][_]) < (m[p[i][_]][_]) ? (m[i][_]) : (m[p[i][_]][_]);
    }
  for (int i = 0; i < n; i++) {
    a2 = 100000000000000;
    a1 = 0;
    int cur = i;
    for (int _ = 0; _ < 40; _++)
      if (k[_]) {
        a1 += s[cur][_];
        a2 = (a2) < (m[cur][_]) ? (a2) : (m[cur][_]);
        cur = p[cur][_];
      }
    printf("%I64d %I64d\n", a1, a2);
  }
  return 0;
}