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)

for i in 0...n
    a[i] -= 1
end

visited = Array.new(n, false)
order = []

order.push(0)
len = nil 
d1 = nil
for i in 1..n
    nxt = a[order[i-1]]
    p nxt
    if visited[nxt]
        len = i
        for j in 0...n
            if nxt == order[j]
                d1 = j
                break
            end
        end
        break
    else
        order.push(nxt)
        visited[nxt] = true
    end
end

if len 
    if len == 1
        #p "A"
        puts order[0] + 1
    else
        d2 = len - d1
        #p "B len:#{len} d1:#{d1} d2:#{d2}"
        kk = (k - d1) % d2
        puts order[d1 + kk] + 1
    end
else
    #p "C"
    puts order[k-1] + 1
end