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>
long long read() {
  static int ch;
  static long long x;
  while (isspace(ch = getchar())) {
  }
  x = ch ^ 48;
  while (isdigit(ch = getchar())) x = (((x << 2) + x) << 1) + (ch ^ 48);
  return x;
}
int af1[100010], af2[100010], af[100010], amin1[100010], amin2[100010],
    amin[100010];
long long asum1[100010], asum2[100010], asum[100010];
int *f1 = af1, *f2 = af2, *min1 = amin1, *min2 = amin2;
long long *sum1 = asum1, *sum2 = asum2;
int main() {
  const int n = read();
  long long k = read();
  for (int i = 0; i < n; ++i) {
    f1[i] = read();
    af[i] = i;
    amin[i] = 0x7fffffff;
  }
  for (int i = 0; i < n; ++i) sum1[i] = min1[i] = read();
  while (k) {
    std::swap(f1, f2);
    std::swap(min1, min2);
    std::swap(sum1, sum2);
    if (k & 1) {
      for (int i = 0; i < n; ++i) {
        amin[i] = std::min(amin[i], min2[af[i]]);
        asum[i] += sum2[af[i]];
        af[i] = f2[af[i]];
      }
    }
    for (int i = 0; i < n; ++i) {
      f1[i] = f2[f2[i]];
      min1[i] = std::min(min2[i], min2[f2[i]]);
      sum1[i] = sum2[i] + sum2[f2[i]];
    }
    k >>= 1;
  }
  for (int i = 0; i < n; ++i) {
    printf("%lld %d\n", asum[i], amin[i]);
  }
  return 0;
}