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 abc167d
      implicit none
      integer(8)::n
      integer(8),allocatable,dimension(:)::a,s,flag,flag_turn
      integer(8)::k
      integer(8)::i
      integer(8)::num_to_loop,num_loop

         read *, n,k
         allocate(a(n),s(0:n),flag(n),flag_turn(n))
         read *, a(1:n)

         s(0)=1; flag=0; flag(1)=1; flag_turn=0; flag_turn(1)=0
         do i=1,n
            s(i)=a(s(i-1))
            if (flag(s(i))/=1) then  ! if not visited
               flag(s(i))=1          ! marking 'visited'
               flag_turn(s(i))=i
            else             
               num_to_loop=i
               num_loop=i-flag_turn(s(i))
               exit
            end if
         end do

         if (num_to_loop>=k) then
            print *, s(k)
         else
            print *, s( mod( k - num_to_loop, num_loop ) + &
                     ( num_to_loop - num_loop) )
         end if

   end program abc167d