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 main
  
  implicit none
  integer(16) :: n, k, i, now, cyc,tmp, num
  integer(16),allocatable :: a(:), b(:), bo(:), cnt(:)
  
  read(*,*) n,k
  allocate(a(n))
  allocate(b(n))
  allocate(bo(n))
  allocate(cnt(n))
  read(*,*) a
  
  ! initialize  
  b  = 0
  bo = 0
  cyc = 0
  cnt = 0
  num = 0

  now = 1
  b(now) = 0
  bo(now) = 0
  cnt(now) = 1

  if( k > n ) then
    do i = 1, k+1
      cnt(a(now)) = cnt(a(now)) + 1
      if( cnt(a(now)) == 2 )then
        cyc = i - bo(a(now))
        num = 1
        exit
      end if
      now = a(now)
      b(now) = i
      bo(now) = b(now)
    end do
    !print*, cyc, now, b(now), bo(a(now)), bo(now), k

    if( num == 1 ) then
      !print*, mod(k-b(now),cyc)
      do i = 1, mod(k-b(now),cyc)
        now = a(now)
      end do
    end if
  else
    now = 1
    do i = 1, k
      now = a(now)
    end do
  end if
  
  print*, now
  
  
end program main