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 ABC167_D
  integer(8)::N,K,X,Y,Z
  integer(8),allocatable::A(:),S(:),T(:)
  read(*,*)N,K
  allocate(A(N),S(N),T(N))
  read(*,*)A
  M=1
  L=1
  S=0
  T=0
  T(1)=1
  S(1)=1
  do i=1,N
     M=A(M)
     S(M)=S(M)+1
     if(S(M)==2) then
        do j=1,N
           if(L==M) then
              X=i-j+1
              Y=i
              Z=j
              go to 10
           end if
           L=A(L)
        end do
     end if
  end do
10 if(K>N) then
      K=mod(K-Z+1,X)+Z-1
      end if
      
      
  M=1
  do i=1,K
     M=A(M)
  end do
  write(*,*)M
end program ABC167_D