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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
        "fmt"
)

func solution(n, k int, a []int) int {
        visit := make([]int, 0)
        hop := make([]int, n+1)
        for i := range hop {
                hop[i] = -1
        }

        cur := 1
        c := 1
        l := 0
        for hop[cur] == -1 {
                hop[cur] = len(visit)
                visit = append(visit, cur)
                cur = a[cur-1]
        }

        c = len(visit) - hop[cur]
        l = hop[cur]
        ans := 0
        if k < l {
                ans = visit[k]
        } else {
                k -= l
                k %= c
                ans = visit[l+k]
        }
        return ans
}

func main() {
        var n, k int
        fmt.Scan(&n, &k)
        a := make([]int, 0, n)
        for i := 0; i < n; i++ {
                tmp := 0
                fmt.Scan(&tmp)
                a = append(a, tmp)
        }
        fmt.Println(solution(n, k, a))
}