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 maxn = 1e5 + 100;
const int maxp2 = 39;
int n;
long long int par[maxn][maxp2];
long long int sum[maxn][maxp2];
long long int minWeight[maxn][maxp2];
void init() {
  for (int j = 1; j <= maxp2 - 1; j++) {
    for (int i = 0; i <= n - 1; i++) {
      par[i][j] = -1;
    }
  }
  for (int j = 1; j <= maxp2 - 1; j++) {
    for (int i = 0; i <= n - 1; i++) {
      if (par[i][j - 1] != -1) {
        par[i][j] = par[par[i][j - 1]][j - 1];
        sum[i][j] = sum[i][j - 1] + sum[par[i][j - 1]][j - 1];
        minWeight[i][j] =
            min(minWeight[i][j - 1], minWeight[par[i][j - 1]][j - 1]);
      }
    }
  }
}
void solve() {
  long long int k;
  scanf("%d", &n);
  scanf("%lld", &k);
  for (int i = 0; i <= n - 1; i++) {
    int to;
    scanf("%d", &to);
    par[i][0] = to;
  }
  for (int i = 0; i <= n - 1; i++) {
    int weight;
    scanf("%d", &weight);
    sum[i][0] = minWeight[i][0] = weight;
  }
  init();
  for (int i = 0; i <= n - 1; i++) {
    long long int s = 0, m = INT_MAX;
    long long int left = k, curNode = i;
    for (int j = maxp2 - 1; j >= 0; j--) {
      if ((1ll << j) <= left) {
        left -= (1ll << j);
        s += sum[curNode][j];
        m = min(m, minWeight[curNode][j]);
        curNode = par[curNode][j];
      }
    }
    printf("%lld %lld\n", s, m);
  }
}
int main() {
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}