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 <iostream>
#include <vector>
#include <list>
#include <algorithm>
#include <cmath>

#define llong long long
#define rep(i,l,n) for(llong (i)=(l);(i)<(n);(i++))
#define _min(a,b) ((a)<(b)?(a):(b))
#define _max(a,b) ((a)>(b)?(a):(b))
#define _abs(a) ((a)>0?(a):(-(a)))

using namespace std;

llong max3(llong*,llong);

int main(){
	int N,K;
	cin >> N >> K;
	int P[N],C[N];
	rep(i,0,N){
		cin >> P[i];
		P[i] -= 1;
	}
	rep(i,0,N) cin >> C[i];
	
	llong ans=-1000000000;
	rep(i,0,N){
		int n = i;
		llong score = 0,max = C[P[n]];
		rep(j,1,K+1){
			n = P[n];
			score += C[n];
			max = _max(max,score);
			if( n == i ){
				if( score < 0 ) break;
              	max = _max(max,max+score*((K/j)-1));
				score *=(K/j);
				j = (K/j)*j;
			}
		}
		ans = _max(ans,max);
	}
	
	cout << ans;
}
