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: Time Limit Exceeded)

function solve()
    n, k = [parse(Int, x) for x in split(readline())]
    a = [parse(Int, x) for x in split(readline())]

    current = 1
    path = [1]

    while a[current] ∉ path
        current = a[current]
        append!(path, current)
    end
    append!(path, a[current])

    if k < length(path)
        path[k+1]
    else
        cycle_start = findfirst(x->(x==path[end]), path)
        k = k - cycle_start
        path = path[cycle_start+1:end]
        k = k % length(path) + 1
        path[k]
    end
end

println(solve())