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>
using namespace std;
typedef long long ll;
const ll INF = 0x3f3f3f3f3f3f3f3f;
#define rep(i, a, b) for(int i = int(a); i <= int(b); i++)
#define N 5005
int P[N], C[N];
int main() {
	int n, k;
	cin >> n >> k;
	for(int i = 1; i <= n; i++) cin >> P[i];
	for(int i = 1; i <= n; i++) cin >> C[i];
	ll Ans = -INF;
	rep(i, 1, n) {
		int p = i;
		ll cnt = 0, len = 0, allsum = 0, sum = 0;
		while(1) {
			++len;allsum += C[p];p = P[p];
			if(p == i)break;
		}
		cnt = 0, sum = 0;
		while(1) {
			++cnt;sum += C[p];
			if(cnt > k)break;
			ll num = (k - cnt) / len;
			ll scr = sum + max(0LL, allsum) * num;
			Ans = max(Ans, scr);
			
			p = P[p];if(p == i)break;
		}
		
	}
	cout << Ans << endl;
	return 0;
} 