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 (LuaJIT 2.1.0) (judge verdict: Wrong Answer)

local N = io.read("*n")
local K = 0LL + io.read("*n")

local A = {}
for i = 1, N do
	A[i] = io.read("*n")
end

local function goToK(town, rem_times)
	if rem_times <= 0 then
		return town
	else
		return goToK(A[town], rem_times - 1)
	end
end

local have_comes = {}
local function teleport(town, times)
	if times == K then
		return town
	end
	local last_time = have_comes[town]
	if last_time ~= nil then
		local K_in_loop = K - last_time
		local loop_times = times - last_time
		K_in_loop = K_in_loop % loop_times
		return goToK(town, K_in_loop)
	else
		have_comes[town] = times
		return teleport(A[town], times + 1)
	end
end

print(teleport(1, 0))