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)

function f()
    n,k=map(x->parse(Int,x),split(readline()))
    ni=zeros(Int,n)
    ni=map(x->parse(Int,x),split(readline()))
    flag=fill(-1,n)
    h=fill(-1,n)
    j=1
    c=0
    for i=1:k
        flag[j]=1
        c += 1
        j=ni[j]
        if flag[j] == 1
            s=1
            jn=j
            h[1]=jn
            j=ni[j]
            b=2
            while jn != j
                h[b]=j
                j=ni[j]
                b += 1
                s += 1
            end
            ansj=(k-c)%s
            println(h[ansj+1])
            exit()
        end
    end   
end
f()