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 <cstdio>
#include <algorithm>
#define LL long long
#define maxn 5010
using namespace std;
LL p[maxn],c[maxn],t[maxn],d[maxn],mid[maxn];
int main(){
	int n,k,i,now,cnt;
	LL mx=-1000000000,val;
	scanf("%d%d",&n,&k);
	for(i=1;i<=n;i++)scanf("%lld",&p[i]);
	for(i=1;i<=n;i++)scanf("%lld",&c[i]);
	for(i=1;i<=n;i++){
		now=p[i],d[i]=c[now],t[i]=1,mid[i]=-1000000000,mid[i]=max(d[i],mid[i]);
		while(1){
			if(now==i)break;
			t[i]++,now=p[now],d[i]+=c[now],mid[i]=max(d[i],mid[i]);
		}
	}
	for(i=1;i<=n;i++){
		if(k/t[i]>0){
			mx=max(mx,mid[i]);
			if(k%t[i]==0){mx=max(mx,(k/t[i]-1)*d[i]+mid[i]);continue;}
		}
		val=k/t[i]*d[i];
		now=p[i],val+=c[now],mx=max(mx,val),cnt=1;
		while(1){
			if(k%t[i]==cnt)break;
			cnt++,now=p[now],val+=c[now],mx=max(mx,val);
		}					
	}
	printf("%lld\n",mx);
	return 0;
}