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(8) :: N,K
  integer(8),allocatable :: A(:)
  integer(8),allocatable :: num(:)
  logical,allocatable :: flag(:)
  integer(8) :: loopnum
  integer(8) :: now, loop_start, now_save
  integer(8) :: step
  integer(8) :: i,j
  
  read(*,*) N,K
  allocate(A(N))
  read(*,*) A(:)
  allocate(flag(N))
  allocate(num(N))
  flag(:) = .false.
  flag(1) = .true.
  num(1) = 0
  now = 1
  now = A(now)
  do i = 1,N+1
     if ( flag(now) ) then
        exit
     else 
        flag(now) = .true.
        num(now) = i
        now = A(now)
     end if
  end do
  ! loop num
  loopnum = i - num(now)
  now_save = now
  now = 1
  do i = 1,N
     now = A(now)
     if (now == now_save ) exit
  end do
  if (  K  <= (loopnum + i) ) then
     now = 1
     do i = 1,K
        now = A(now)
     end do
     write(*,'(i0)') now
     stop
  end if
  !write(*,*) loopnum
  step = mod( K-num(now), loopnum )
  !write(*,*) now,step
  now = now_save
  do i = 1,step
     !num(int(now)) = i
     now = A(now)
  end do
  write(*,'(i0)') now
end program main