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
from sys import stdin
nii=lambda:map(int,stdin.readline().split())
lnii=lambda:list(map(int,stdin.readline().split()))

n,k=nii()
p=lnii()
c=lnii()

ans=-10**18
for i in range(n):
  ini_x=i
  x=i
  point=[]

  t_ans=0
  cnt=0
  t_max=-10**18
  while True:
    x=p[x]-1
    t_point=c[x]
    point.append(t_point)
    t_ans+=t_point
    t_max=max(t_max,t_ans)
    cnt+=1
    if x==ini_x:
      break

  if t_ans<0:
    ans=max(ans,t_max)
  else:
    num=k//cnt
    num-=1
    c_ans=t_ans*num
    c_max=c_ans
    zan=k-(num*cnt)
    for j in range(zan):
      x=p[x]-1
      c_ans+=c[x]
      c_max=max(c_max,c_ans)
    ans=max(ans,c_max)

print(ans)