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)

// +build ignore
package main

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

// I/O
type Scanner struct {
	sc *bufio.Scanner
}

func NewScanner() *Scanner {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 1024), int(1e+9))
	return &Scanner{sc}
}

func (s *Scanner) nextStr() string {
	s.sc.Scan()
	return s.sc.Text()
}

func (s *Scanner) nextInt() int {
	i, e := strconv.Atoi(s.nextStr())
	if e != nil {
		panic(e)
	}
	return i
}

func (s *Scanner) nextFloat() float64 {
	f, e := strconv.ParseFloat(s.nextStr(), 64)
	if e != nil {
		panic(e)
	}
	return f
}

func (s *Scanner) nextRuneSlice() []byte {
	return []byte(s.nextStr())
}

func (s *Scanner) nextIntSlice(n int) []int {
	res := make([]int, n)
	for i := 0; i < n; i++ {
		res[i] = s.nextInt()
	}
	return res
}

func (s *Scanner) nextFloatSlice(n int) []float64 {
	res := make([]float64, n)
	for i := 0; i < n; i++ {
		res[i] = s.nextFloat()
	}
	return res
}

func gcd(x, y int) int {
	if x%y != 0 {
		return gcd(y, x%y)
	}
	return y
}

const D = 60

func run(input io.Reader, output io.Writer) int {
	sc := NewScanner()
	N := sc.nextInt()
	K := sc.nextInt()
	A := make([]int, N)
	for i := 0; i < N; i++ {
		A[i] = sc.nextInt() - 1
	}

	T := make([][]int, D)
	T[0] = make([]int, N)
	for i := 0; i < N; i++ {
		T[0][i] = A[i]
	}

	for i := 1; i < D; i++ {
		T[i] = make([]int, N)
		for j := 0; j < N; j++ {
			T[i][j] = T[i-1][T[i-1][j]]
		}
	}

	p := 0
	for i := D; i >= 0; i-- {
		if K&(1<<i) != 0 {
			p = T[i][p]
		}
	}

	fmt.Println(p + 1)

	return 0
}

func main() {
	os.Exit(run(os.Stdin, os.Stdout))
}