Codeforces Educational Codeforces Round 15 E - Analysis of Pathes in Functional Graph

E. Analysis of Pathes in Functional Graph

time limit per test

2 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

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, ..., f_n - 1, where f_i — 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, ..., w_n - 1, where w_i — the arc weight from i to f_i.

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 s_i and m_i, where:

• s_i — the sum of the weights of all arcs of the path with length equals to k which starts from the vertex i;
• m_i — 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, ..., f_n - 1 (0 ≤ f_i < n) and the third — the sequence w₀, w₁, ..., w_n - 1 (0 ≤ w_i ≤ 10⁸).

Output

Print n lines, the pair of integers s_i, m_i 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

题目链接：http://codeforces.com/contest/702/problem/E

 #include<bits/stdc++.h>
 #define ll long long
 #define FOR(i,a,b) for(i=a;i<=b;i++)
 using namespace std;
 ll f[][],sum,w[][],s[][];
 int main() {

     ll i,j,k,x,m,n;
     cin>>n>>k;
     FOR(i,,n-)
         cin>>f[i][];
     FOR(i,,n-)
     {
         cin>>w[i][];
         s[i][]=w[i][];
     }
     FOR(j,,)
         FOR(i,,n-)
         {
             f[i][j]=f[f[i][j-]][j-];
             w[i][j]=min(w[i][j-],w[f[i][j-]][j-]);
             s[i][j]=s[i][j-]+s[f[i][j-]][j-];
         }

     FOR(i,,n-)
     {
         m=w[i][];
         x=i;
         sum=;
         FOR(j,,)
         {
             if(k&1LL<<j)
             {
                 sum+=s[x][j];
                 m=min(m,w[x][j]);
                 x=f[x][j];
             }
         }
         cout<<sum<<" "<<m<<endl;
     }
     return ;
 }