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.(Int,split(readline()))
    A = parse.(Int,split(readline()))
    g_town = zeros(Int,N)
    reachs = zeros(Bool,N)
    p = 1
    first = second = -1
    for i in 1:N
        reachs[p] = true
        g_town[i] = p
        p = A[p]
        if reachs[p]
            first = findfirst(isequal(p),g_town)
            second = i+1
            g_town[second] = p
            break
        end
    end
    if K < second
        print(g_town[K+1])
    else
        k = K-first+1
        n = second - first
        print(g_town[first+k%n])
    end
end
main()