Problem:
Score: 400 points

Problem Statement

The Kingdom of Takahashi has N towns, numbered 1 through N.

There is one teleporter in each town. The teleporter in Town i (1 \leq i \leq N) sends you to Town A_i.

Takahashi, the king, loves the positive integer K. The selfish king wonders what town he will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Help the king by writing a program that answers this question.

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq N

1 \leq K \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N K
A_1 A_2 \dots A_N

Output

Print the integer representing the town the king will be in if he starts at Town 1 and uses a teleporter exactly K times from there.

Sample Input 1

4 5
3 2 4 1

Sample Output 1

4

If we start at Town 1 and use the teleporter 5 times, our travel will be as follows: 1 \to 3 \to 4 \to 1 \to 3 \to 4.

Sample Input 2

6 727202214173249351
6 5 2 5 3 2

Sample Output 2

2

Solution in Lua (Lua 5.3.5) (judge verdict: Accepted)

local n, k = io.read("*n", "*n")
local a = {}
for i = 1, n do
  a[i] = io.read("*n")
end
local map = {}
local len = 0
map[1] = 0
local src = 1
local rem = 0
while true do
  len = len + 1
  local dst = a[src]
  if len == k then
    print(dst)
    os.exit()
  end
  if map[dst] then
    local offset = map[dst]
    local loopSize = len - offset
    rem = k - offset
    rem = rem % loopSize
    src = dst
    break
  else
    map[dst] = len
  end
  src = dst
end
for i = 1, rem do
  local dst = a[src]
  src = dst
end
print(src)