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: Wrong Answer)

function main()
	N,K=map(x->parse(Int,x),split(readline()))
	A=map(x->parse(Int,x),split(readline()))
	vis=-ones(Int,N)
	now=1
	cnt=0
	pre=Int[]
	while vis[now]==-1
		vis[now]=cnt
		cnt+=1
		push!(pre,now)
		now=A[now]
	end
	if K<vis[now]
		println(pre[K])
	else
		K-=vis[now]
		K%=cnt-vis[now]
		println(pre[vis[now]+K+1])
	end
end
main()