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)
parseBigInt(x) = parse(BigInt, x)
parseFloat(x) = parse(Float64, x)
parseBigFloat(x) = parse(BigFloat, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
    n,k=parseMap(split(readline()))
    a=parseMap(split(readline()))
    INF=2<<32
    visited=[INF for i in 1:n]
    visited[1]=0
    now=1
    loop=(1,n)
    for i in 1:1000000
        if visited[a[now]]<INF
            loop=(a[now],now)
            break
        end
        visited[a[now]]=visited[now]+1
        now=a[now]
    end
    if visited[loop[1]]>k
        println(findfirst(x->x==k,visited))
    else
        if loop[2]-loop[1]==0
            res=0
        else
            res=k%(visited[loop[2]]-visited[loop[1]]+1)
        end
        println(findfirst(x->x==visited[loop[1]]+res,visited))
    end
end
main()