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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

program free
	implicit none
	integer(8):: n,k,ans,loop,machi=1,count=0,i
	integer(8),allocatable :: a(:),trace(:)
	read (*,*) n,k
	allocate(a(n))
	allocate(trace(n+1))
	do i=1,n+1
    	trace(i)=0
    end do
	read (*,*) a
	do i=1,k
		count=count+1
		if(trace(machi)/=0) exit
		trace(machi)=i
		machi=a(machi)
	end do
	if(count==2) then
		write (*,'(i0)') 1
	else if(count==k) then
		write (*,'(i0)') machi
	else
		loop=count-trace(machi)
		ans=mod(k-trace(machi)+1,loop)
		do i=1,ans
			machi=a(machi)
		end do
		write (*,'(i0)') machi
	end if
	end program free