Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 2
2 4 5 1 3
3 4 -10 -8 8

Sample Output 1

8

When we start at some square of our choice and make at most two moves, we have the following options:

If we start at Square 1, making one move sends the piece to Square 2, after which the score is 4. Making another move sends the piece to Square 4, after which the score is 4 + (-8) = -4.

If we start at Square 2, making one move sends the piece to Square 4, after which the score is -8. Making another move sends the piece to Square 1, after which the score is -8 + 3 = -5.

If we start at Square 3, making one move sends the piece to Square 5, after which the score is 8. Making another move sends the piece to Square 3, after which the score is 8 + (-10) = -2.

If we start at Square 4, making one move sends the piece to Square 1, after which the score is 3. Making another move sends the piece to Square 2, after which the score is 3 + 4 = 7.

If we start at Square 5, making one move sends the piece to Square 3, after which the score is -10. Making another move sends the piece to Square 5, after which the score is -10 + 8 = -2.

The maximum score achieved is 8.

Sample Input 2

2 3
2 1
10 -7

Sample Output 2

13

Sample Input 3

3 3
3 1 2
-1000 -2000 -3000

Sample Output 3

-1000

We have to make at least one move.

Sample Input 4

10 58
9 1 6 7 8 4 3 2 10 5
695279662 988782657 -119067776 382975538 -151885171 -177220596 -169777795 37619092 389386780 980092719

Sample Output 4

29507023469

The absolute value of the answer may be enormous.

Solution in Lua (LuaJIT 2.1.0) (judge verdict: Accepted)

local mfl, mce = math.floor, math.ceil
local n, k = io.read("*n", "*n")
assert(-1000000000 <= k and k <= 1000000000)
local p, c = {}, {}
for i = 1, n do
  p[i] = io.read("*n")
end
for i = 1, n do
  c[i] = io.read("*n")
  assert(-1000000000 <= c[i] and c[i] <= 1000000000)
end
local asked = {}
for i = 1, n do
  asked[i] = false
end
local zpos = 1
local function findstart()
  for i = zpos, n do
    if not asked[i] then zpos = i + 1 return i end
  end
  return false
end
local ret = -1000000007LL
local function mma_l(a, b) return a < b and b or a end
while true do
  local spos = findstart()
  if not spos then break end
  local route = {spos}
  local sum = 0LL + c[spos]
  local src = spos
  asked[spos] = true
  while true do
    local dst = p[src]
    if asked[dst] then break end
    asked[dst] = true
    table.insert(route, dst)
    sum = sum + c[dst]
    src = dst
  end
  local len = #route
  if 0LL < sum then
    local lp = mfl(k / len)
    local rem = k
    if 1 <= lp then
      lp = lp - 1
      rem = k - lp * len
    end
    sum = sum * lp
    ret = mma_l(ret, sum)
    for i = 1, len do
      local v = 0LL
      local src = route[i]
      for j = 1, rem do
        local dst = p[src]
        v = v + c[dst]
        ret = mma_l(ret, sum + v)
        src = dst
      end
    end
  else
    for i = 1, len do
      local v = 0LL
      local src = route[i]
      local lim = math.min(len, k)
      for j = 1, lim do
        local dst = p[src]
        v = v + c[dst]
        ret = mma_l(ret, v)
        src = dst
      end
    end
  end
end
ret = tostring(ret):gsub("LL", "")
print(ret)