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>
typedef int iarrN[100003][35];
struct IO {
  template <typename T>
  inline IO operator>>(T &n) {
    n = 0;
    char c = getchar();
    while (c < '0' || c > '9') c = getchar();
    while (c >= '0' && c <= '9')
      n = (n << 3) + (n << 1) + (c ^ 48), c = getchar();
    return *this;
  }
} cin;
constexpr int MX = 33, inf = 0x3f3f3f3f;
int N, son[100003][35], mnw[100003][35];
long long K, sw[100003][35];
void init() {
  cin >> N >> K;
  for (int i = 1; i <= N; ++i) cin >> son[i][0], ++son[i][0];
  for (int i = 1; i <= N; ++i) cin >> mnw[i][0], sw[i][0] = mnw[i][0];
  for (int j = 1; j <= MX; ++j)
    for (int i = 1; i <= N; ++i) {
      son[i][j] = son[son[i][j - 1]][j - 1];
      sw[i][j] = sw[i][j - 1] + sw[son[i][j - 1]][j - 1];
      mnw[i][j] = std::min(mnw[i][j - 1], mnw[son[i][j - 1]][j - 1]);
    }
}
inline void query(int u) {
  int ansmn = inf;
  long long k = K, anss = 0;
  for (int i = MX; i >= 0; --i)
    if (k >= (1ll << i)) {
      k -= 1ll << i;
      anss += sw[u][i];
      ansmn = std::min(ansmn, mnw[u][i]);
      u = son[u][i];
    }
  printf("%I64d %d\n", anss, ansmn);
}
int main() {
  init();
  for (int i = 1; i <= N; ++i) query(i);
  return 0;
}