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 Lua (Lua 5.3.5) (judge verdict: Accepted)

n,k=io.read("*n","*n","*l")
a={}
for i=1,n do
    a[i]=io.read("*n")
end

path={1}
visited={}
position=1
for i=1,n do
    table.insert(path,a[position])
    if not visited[position] then
        visited[position]=true
    else
        break
    end
    if i==k then
        print(a[position])
        return
    end
    position=a[position]
end

loop=0
distance=0
for i=1,#path do
    if path[i]==a[position] then
        loop=#path-i
        distance=i-2
        break
    end
end

x=(k-distance)%loop
for i=1,x do
    position=a[position]
end
print(position)