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: Wrong Answer)

n,k = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)
b = Array.new(n, 0)
b[0] = 1
nex = 0
roop = 0
offset = 0
ans = 0
k.times do |i|
    if b[a[nex]-1] == 0
        b[a[nex]-1] = i+2
        nex = a[nex]-1
    else
        roop = i - b[a[nex]-1] + 2
        offset = b[a[nex]-1]-1
        rem = (k - offset)%roop
        ans = b.index(b[a[nex]-1]+rem)+1        
        break
    end
    if i == k
        ans = nex+1
    end
end
puts ans