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 Julia (1.4.0) (judge verdict: Runtime Error)

const double = Float64
const int = Int64
const vint = Vector{int}
const vdouble = Vector{double}

int(x) = parse(int,x)
parseint(x) = parse(int, x)
readint() = map(parseint, split(readline()))

function main()
  n, k = readint()
  a = Vector{int}(undef,n)
  a .= readint()

  kita = falses(n)

  K = zeros(int,n+1)
  s = 1
  t = 1

  K[1] = 1
  B = zeros(int,n)
  B[1] = 1

  c = 0
  for i in 1:n
    t = a[i]
    K[i] = s
    B[s] = i
    K[i+1] = t 
    B[s] = i+1

    kita[s] = true
    if kita[t]
      x = B[t]
      y = i

      if k <= y
        println(K[k+1])
      else 
        println(K[x+ (k-i)%(y-x+1)])
      end
      return      
    end
    s = t
  end
end

main()