#include<cstdio>
#include<iostream>
#include<vector>
using namespace std;
#define ll long long
int n;
ll k;
const int Maxn=5005;
int p[Maxn];
ll c[Maxn];

void calc(int now,vector<ll>&vv){
	ll sum=0;
	int at=now;
	for(int i=1;i<=n;i++){
		sum+=c[p[at]];
		vv.push_back(sum);
		at=p[at];
		if(at==now)return;
	}
}
int main(){
	scanf("%d%lld",&n,&k);
	for(int i=0;i<n;i++){
		scanf("%d",&p[i]);
		p[i]--;
	}
	for(int i=0;i<n;i++)scanf("%lld",&c[i]);
	ll ans=-1e17;
	for(int i=0;i<n;i++){
		vector<ll>vv;
		calc(i,vv);
		for(int j=1;j<=min((ll)vv.size(),k);j++){
			ans=max(ans,vv[j-1]+(k-j)/(ll)vv.size()*(vv.back()>0?vv.back():0));
		}
	}
	printf("%lld\n",ans);
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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<cstdio>
#include<iostream>
#include<vector>
using namespace std;
#define ll long long
int n;
ll k;
const int Maxn=5005;
int p[Maxn];
ll c[Maxn];

void calc(int now,vector<ll>&vv){
	ll sum=0;
	int at=now;
	for(int i=1;i<=n;i++){
		sum+=c[p[at]];
		vv.push_back(sum);
		at=p[at];
		if(at==now)return;
	}
}
int main(){
	scanf("%d%lld",&n,&k);
	for(int i=0;i<n;i++){
		scanf("%d",&p[i]);
		p[i]--;
	}
	for(int i=0;i<n;i++)scanf("%lld",&c[i]);
	ll ans=-1e17;
	for(int i=0;i<n;i++){
		vector<ll>vv;
		calc(i,vv);
		for(int j=1;j<=min((ll)vv.size(),k);j++){
			ans=max(ans,vv[j-1]+(k-j)/(ll)vv.size()*(vv.back()>0?vv.back():0));
		}
	}
	printf("%lld\n",ans);
	return 0;
}
```