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)

function main()
    N,K=parse.(Int64,split(readline()))
    A=parse.(Int64,split(readline()))
    logK::Int64=1
    while ((1<<logK) < K)
        logK+=1
    end
    doubling=zeros(Int64,logK,N)
    for i in 1:N
        global doubling[1,i]=A[i]
    end
    for t=1:logK-1
        for i=1:N
            global doubling[t+1,i]=doubling[t,doubling[t,i]]
        end
    end
    
    now::Int64=1
    k::Int64=1
    
    while K>0
        if K&1==1
            now=doubling[k,now]
            
        end
        K=K>>1
        k+=1
    end
    println(now)
end

main()