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: Accepted)

parseLine(str) = parse.(Int, split(str))

function solve()
    N, K = parseLine(readline())
    A = parseLine(readline())
    cycle = Vector{Int}()
    cur = A[1]; length = 0
    seen = zeros(Bool, N)
    while true
        seen[cur] == true && break
        seen[cur] = true
        push!(cycle, cur)
        length += 1
        cur = A[cur]
    end
    start = findfirst(isequal(cur), cycle)
    C = length - start + 1
    ai = (K <= length) ? K : start+(K-start)%C
    println(cycle[ai])
end

solve()