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: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func scanInt() int {
	sc.Scan()
	iv, _ := strconv.Atoi(sc.Text())
	return iv
}

func init() {
	sc.Split(bufio.ScanWords)
}

func main() {
	n, k := scanInt(), scanInt()
	a := make([]int, n+1)
	for i := 1; i <= n; i++ {
		a[i] = scanInt()
	}

	p := 1
	ans := make([]int, n+1)
	ans[0] = p
	passed := make(map[int]int)
	passed[p] = 0
	var r int
	for i := 1; i <= n; i++ {
		p = a[p]
		if _, ok := passed[p]; ok {
			k -= passed[p]
			r = i - passed[p] - 1
			break
		}

		passed[p] = i
		ans[i] = p
		if i == k {
			fmt.Println(p)
			return
		}
	}

	k %= r
	fmt.Println(ans[k+1])
}