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 = io.read("*n")
local k = io.read("*n"
)
io.read("*l")
local towns = {}
for i = 1, n do 
	towns[i] = io.read("*n")
end
io.read("*l")
local visited = {}
local step = 1
local idx = 1
local period
local periodstart
local steps = {}
while(step <= k) do 
	if visited[towns[idx]] then
		period = step - visited[towns[idx]]
		periodstart = visited[towns[idx]]
		break
	end
	visited[towns[idx]] = step
	steps[step] = towns[idx]
	idx = towns[idx]
	step = step + 1
end
if period then 
	local resttimes = k - step
	resttimes = resttimes % period
	print(steps[periodstart + resttimes])
else
	print(idx)
end