#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using P = pair<int,int>;
using ll = long long;

int main() {
  int N, K;
  cin >> N >> K;
  
  vector<int> P(N), C(N);
  rep(i,N) cin >> P[i];
  rep(i,N) cin >> C[i];
  rep(i,N) P[i]--; // 0始まりに合わせる
  
  ll ans = -1e18; //負にしておく
  rep(si, N){ // 開始位置の変更
    int x = si;
    vector<int> s;
    ll tot = 0; 
    // 周期のカウント
    while(1) {
      x = P[x]; // 移動後の位置
      s.push_back(C[x]); // 周期内のスコア追加
      tot += C[x];
      if (x==si) break;
    }
    int l = s.size();
    ll t = 0; // 累積和
    rep(i,l) { // 1周期分の試行
      t += s[i];
      if (i+1 > K) break;
      ll now = t;
      if (tot > 0) { // totが負になる場合周期を繰り返さない方がいい
        ll e = (K-i-1)/l; // 何周できるか
        now += tot*e;
      }
      ans = max(ans, now);
    }
  }
  
  cout << ans << endl;
  
  return 0;
}
### Prompt

Your task is to create a CPP solution to the following problem:

Takahashi will play a game using a piece on an array of squares numbered 1, 2, \cdots, N. Square i has an integer C_i written on it. Also, he is given a permutation of 1, 2, \cdots, N: P_1, P_2, \cdots, P_N.

Now, he will choose one square and place the piece on that square. Then, he will make the following move some number of times between 1 and K (inclusive):

* In one move, if the piece is now on Square i (1 \leq i \leq N), move it to Square P_i. Here, his score increases by C_{P_i}.



Help him by finding the maximum possible score at the end of the game. (The score is 0 at the beginning of the game.)

Constraints

* 2 \leq N \leq 5000
* 1 \leq K \leq 10^9
* 1 \leq P_i \leq N
* P_i \neq i
* P_1, P_2, \cdots, P_N are all different.
* -10^9 \leq C_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
P_1 P_2 \cdots P_N
C_1 C_2 \cdots C_N


Output

Print the maximum possible score at the end of the game.

Examples

Input

5 2
2 4 5 1 3
3 4 -10 -8 8


Output

8


Input

2 3
2 1
10 -7


Output

13


Input

3 3
3 1 2
-1000 -2000 -3000


Output

-1000


Input

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719


Output

29507023469

### Response

```cpp
#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using P = pair<int,int>;
using ll = long long;

int main() {
  int N, K;
  cin >> N >> K;
  
  vector<int> P(N), C(N);
  rep(i,N) cin >> P[i];
  rep(i,N) cin >> C[i];
  rep(i,N) P[i]--; // 0始まりに合わせる
  
  ll ans = -1e18; //負にしておく
  rep(si, N){ // 開始位置の変更
    int x = si;
    vector<int> s;
    ll tot = 0; 
    // 周期のカウント
    while(1) {
      x = P[x]; // 移動後の位置
      s.push_back(C[x]); // 周期内のスコア追加
      tot += C[x];
      if (x==si) break;
    }
    int l = s.size();
    ll t = 0; // 累積和
    rep(i,l) { // 1周期分の試行
      t += s[i];
      if (i+1 > K) break;
      ll now = t;
      if (tot > 0) { // totが負になる場合周期を繰り返さない方がいい
        ll e = (K-i-1)/l; // 何周できるか
        now += tot*e;
      }
      ans = max(ans, now);
    }
  }
  
  cout << ans << endl;
  
  return 0;
}
```