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;
long long n, k;
long long dp1[100005][40], dp2[100005][40], dp3[100005][40];
long long ans1[100005], ans2[100005];
int main() {
  scanf("%lld", &n);
  scanf("%lld", &k);
  for (int i = 0; i < n; i++) {
    scanf("%lld", &dp1[i][0]);
  }
  for (int i = 0; i < n; i++) {
    ans2[i] = 2e10;
    ans1[i] = 0;
    scanf("%lld", &dp2[i][0]);
    dp3[i][0] = dp2[i][0];
  }
  for (int i = 1; i <= 38; i++) {
    for (int j = 0; j < n; j++) {
      dp1[j][i] = dp1[dp1[j][i - 1]][i - 1];
      dp2[j][i] = dp2[j][i - 1] + dp2[dp1[j][i - 1]][i - 1];
      dp3[j][i] = min(dp3[j][i - 1], dp3[dp1[j][i - 1]][i - 1]);
    }
  }
  for (int i = 0; i < n; i++) {
    long long kk = k;
    int u = i;
    for (long long j = 38; j >= 0; j--) {
      if ((kk - ((long long)1 << j)) >= 0) {
        ans1[i] += dp2[u][j];
        ans2[i] = min(ans2[i], dp3[u][j]);
        kk -= ((long long)1 << j);
        u = dp1[u][j];
      }
    }
  }
  for (int i = 0; i < n; i++) {
    printf("%lld %lld\n", ans1[i], ans2[i]);
  }
  return 0;
}