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

var startval int

func solve() {
	n := scanInt()
	k := scanInt()
	a := make([]int, n)
	seen := map[int]bool{}
	trace := []int{0}
	for i := 0; i < n; i++ {
		a[i] = scanInt()
	}
	for i := 0; i < k; i++ {
		next := a[trace[i]] - 1
		_, ok := seen[next]
		if ok {
			startval = next
			break
		}
		trace = append(trace, next)
		seen[next] = true
	}
	var start int
	for i := 0; i < k; i++ {
		if trace[i] == startval {
			start = i
			break
		}
	}
	repetition := trace[start:]
	fmt.Println(repetition[(k-start)%(len(repetition))] + 1)
	return
}

var sc = bufio.NewScanner(os.Stdin)

func scanString() string {
	sc.Scan()
	return sc.Text()
}
func scanInt() int {
	sc.Scan()
	a, err := strconv.Atoi(sc.Text())
	if err != nil {
		fmt.Println(err)
	}
	return a
}
func scanFloat64() float64 {
	f, _ := strconv.ParseFloat(scanString(), 64)
	return f
}
func Permute(nums []int) [][]int {
	n := factorial(len(nums))
	ret := make([][]int, 0, n)
	permute(nums, &ret)
	return ret
}
func permute(nums []int, ret *[][]int) {
	*ret = append(*ret, makeCopy(nums))

	n := len(nums)
	var i, j int
	for {
		for i = n - 2; i >= 0; i-- {
			if nums[i] < nums[i+1] {
				break
			}
		}
		if i < 0 {
			return
		}
		for j = n - 1; ; j-- {
			if nums[j] > nums[i] {
				break
			}
		}
		nums[i], nums[j] = nums[j], nums[i]
		for k, l := i+1, n-1; k < l; {
			nums[k], nums[l] = nums[l], nums[k]
			k++
			l--
		}
		*ret = append(*ret, makeCopy(nums))
	}
}

func factorial(n int) int {
	ret := 1
	for i := 2; i <= n; i++ {
		ret *= i
	}
	return ret
}
func makeCopy(nums []int) []int {
	return append([]int{}, nums...)
}
func gcd(a int, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}
func main() {
	sc.Split(bufio.ScanWords)
	solve()
}