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 Ruby (2.7.1) (judge verdict: Accepted)

n, k = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)

tl = Array.new(n,0)
tl[0] = 1
nxt = a[0]
for i in 1..(n-1)
  tl[i] = nxt
  nxt = a[nxt-1]
end
ck = Array.new(n+1,0)
en = n-1
for i in 0..(n-1)
  if ck[tl[i]] == 0
    ck[tl[i]] += 1
  else
    lps = tl[i]
    en = i-1
  end
end

mg = 0
if en != n-1
  for i in 0..en
    if tl[i] == lps
      break
    else
      mg += 1
    end
  end
end

if k <= n-1
  puts tl[k]
else
  puts tl[mg + (k-mg) % (en+1-mg)]
end