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: Wrong Answer)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
N,K = parseMap(split(readline()))
A = parseMap(split(readline()))

start_city = 1
still_see = Set{Int}()
push!(still_see,1)
if N < K
for i in 1:K
    visit_city = A[start_city]
    if visit_city in still_see
        loop_begin_city = visit_city
        loop_fin_city = start_city
        loop_start_city = loop_fin_city
        loop_arrays = [loop_fin_city,]
        for j in 1:10^6
            loop_visit_city = A[loop_start_city]
            if loop_visit_city == loop_fin_city
                ans_idx = ((K - i) % length(loop_arrays)) - 1
                if ans_idx == 0 
                    return loop_arrays[end]
                elseif ans_idx == -1
                    return loop_arrays[end]
                end
                return loop_arrays[ans_idx]
            else
            end
            push!(loop_arrays,loop_visit_city)
            loop_start_city = loop_visit_city
        end
    else
        push!(still_see,visit_city)
    end
    start_city = visit_city
end
else
    for i in 1:K
        visit_city = A[start_city]
        start_city = visit_city
        if i == K
            return visit_city
        end
    end
end
end


println(main())