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: Wrong Answer)

#!/usr/bin/env -S JULIA_VERSION=1.4.0 julia
# contest: abc167, problem: abc167_d, alphabet: D

function solve(N::Int, K::Int, A::Vector{Int})
  hist = zeros(Int, N+10)
  hist[0+1] = 1
  dic = Dict(1=>0)
  k = 1
  p = A[1]
  while true
    k0 = get!(dic, p, k)
    if k0 < k
      p0 = hist[k0+1]
      m = k - k0
      kK = k0 + (K - k0) % m
      println(hist[kK + 1])
      break
    end
    if p == A[p]
      println(p)
      break
    end
    hist[k+1] = p
    p = A[p]
    k += 1
  end
end

function main()
  tokens = Channel{String}(32)
  Task() do
    for line in eachline(@static VERSION < v"0.6" ? STDIN : stdin)
      startswith(line, '\0') && break
      for token in split(chomp(line))
        put!(tokens, token)
      end
    end
    close(tokens)
  end |> schedule
  N = parse(Int, take!(tokens))
  K = parse(Int, take!(tokens))
  A = similar(Vector{Int}, N)
  for i in 1:N
    A[i] = parse(Int, take!(tokens))
  end
  solve(N, K, A)
end

if isempty(get(ENV, "ATCODER_LOCAL", ""))
  isempty(ARGS) && main()
else
  @eval begin
    const samples = [("4 5\n3 2 4 1", "4"), ("6 727202214173249351\n6 5 2 5 3 2", "2")]
    function test(sampleids...)
      isempty(sampleids) && return test(collect(1:length(samples))...)
      ostdin, ostdout = @static VERSION < v"0.6" ? (STDIN, STDOUT) : (stdin, stdout)
      rd, wr = first(redirect_stdout()), last(redirect_stdin())
      try
        map(sampleids) do sampleid
          input, output = samples[sampleid]
          print(ostdout, "Testing sample #$(sampleid)..."); flush(ostdout)
          println(wr, input)
          println(wr, "\0")
          t = @elapsed main()
          println()
          result = strip(String(readavailable(rd)))
          if result == output
            println(ostdout, "OK ($t sec).")
            true
          else
            println(ostdout, "ERROR ($t sec)")
            println(ostdout, "== expected ==\n$output")
            println(ostdout, "== actual ==\n$result\n")
            false
          end
        end |> all
      finally
        redirect_stdin(ostdin)
        redirect_stdout(ostdout)
      end
    end
    submit() = test() && (prog = @__FILE__; run(`atcoder-submit $prog`))
    !isinteractive() && submit()
  end
end