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 Julia (1.4.0) (judge verdict: Accepted)

parseInt(x)=parse(Int, x)
parseMap(x::Array{SubString{String},1})=map(parseInt, x)

function main()
	n,k = readline() |> split |> parseMap
	a = readline() |> split |> parseMap
	chk = zeros(Int,n)
	now = 1
	ct = 0
	cs = 0
	cl = 0
	while chk[now]==0
		chk[now]=1
		now=a[now]
		ct+=1
	end
	cs = now
	now = a[now]
	cl += 1
	while now!=cs
		now=a[now]
		cl+=1
	end
	if k<ct
		now = 1
		for i in 1:k
			now=a[now]
		end
		println(now)
	else
		k=(k-ct)%cl
		now = cs
		for i in 1:k
			now=a[now]
		end
		println(now)
	end
end

main()