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 + 3;
long long w[N], k, Mn[35][N], Sm[35][N];
int fa[35][N], n;
int main() {
  scanf("%d%lld", &n, &k);
  for (register int i = (1); i <= (n); ++i) scanf("%d", &fa[0][i]), fa[0][i]++;
  for (register int i = (1); i <= (n); ++i)
    scanf("%lld", w + i), Mn[0][i] = Sm[0][i] = w[i];
  for (register int i = (1); i <= (34); ++i)
    for (register int j = (1); j <= (n); ++j)
      fa[i][j] = fa[i - 1][fa[i - 1][j]],
      Mn[i][j] = min(Mn[i - 1][j], Mn[i - 1][fa[i - 1][j]]),
      Sm[i][j] = Sm[i - 1][j] + Sm[i - 1][fa[i - 1][j]];
  for (register int i = (1); i <= (n); ++i) {
    long long s = k - 1, ret = w[i], Met = w[i], p = fa[0][i];
    for (register int i = 0; s; s >>= 1, ++i)
      if (s & 1) ret += Sm[i][p], Met = min(Met, Mn[i][p]), p = fa[i][p];
    printf("%lld %lld\n", ret, Met);
  }
  return 0;
}