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
#include<bits/stdc++.h>
#define int long long
using namespace std;
const int N=5005;
int n,k,p[N],c[N],cir[N];
int cal(int st)
{
	int now=p[st],j=0;
	while(now!=st)
	{
		cir[++j]=c[now];
		now=p[now];
	}
	cir[++j]=c[now];
	for(int i=1;i<=j;i++) 
		cir[i]+=cir[i-1];
	if(k<=j)
	{
		int ans=cir[1];
		for(int i=1;i<=k;i++) 
			ans=max(ans,cir[i]);
		return ans;
	}
	else
	{
		int ans=cir[1];
		for(int i=1;i<=j;i++) 
			ans=max(ans,cir[i]);
		int macir=ans,qu=k%j,maqu=0;
		for(int i=1;i<=qu;i++) 
			maqu=max(maqu,cir[i]);
		ans=max(ans,k/j*cir[j]+maqu);
		if(k/j>0)
			ans=max(ans,(k/j-1)*cir[j]+macir);
		return ans;
	}
}
signed main()
{
	scanf("%lld%lld",&n,&k);
	for(int i=1;i<=n;i++) 
		scanf("%lld",&p[i]);
	for(int i=1;i<=n;i++) 
		scanf("%lld",&c[i]);
	int ans=-1e17;
	for(int i=1;i<=n;i++)
		ans=max(cal(i),ans);
	printf("%lld\n",ans);
	return 0;
}