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"
	"math"
	"os"
)

func main() {
	N, K := ReadInt(), ReadInt()
	A := ReadInts(N)

	maxI := int(math.Ceil(math.Log2(float64(K))))
	next := make([][]int, maxI+1)
	for k := 0; k < maxI+1; k++ {
		next[k] = make([]int, N)
	}
	for i := 0; i < N; i++ {
		next[0][i] = A[i] - 1
	}
	for k := 0; k < maxI; k++ {
		for i := 0; i < N; i++ {
			next[k+1][i] = next[k][next[k][i]]
		}
	}

	ans := 0
	k := 0
	for K > 0 {
		if K&1 == 1 {
			ans = next[k][ans]
		}
		K >>= 1
		k++
	}
	fmt.Println(ans + 1)
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int)       { Scan(&i); return }
func ReadString() (s string) { Scan(&s); return }
func ReadInts(n int) []int {
	v := make([]int, n)
	for i := 0; i < n; i++ {
		Scan(&v[i])
	}
	return v
}