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 main() {
	var n, k int

	fmt.Scanf("%d %d", &n, &k)

	a := make([]int, n+1)
	for i := 1; i <= n; i++ {
		fmt.Scanf("%d", &a[i])
	}

	pos := 1
	prev := pos
	memo := []int{1}
	var i int

	for i = 0; i < k; i++ {
		prev = pos
		pos = a[pos]
		a[prev] = -(i + 1)
		if pos < 0 {
			break
		}
		memo = append(memo, pos)
	}

	if i == k {
		fmt.Println(pos)
	} else {
		j := -pos
		k1 := k - j
		l := len(memo) - j
		mod := k1 % l
		fmt.Println(memo[j+mod])
	}
}