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.Scan(&n, &k)

	as := make([]int, n+1)
	for i := 1; i <= n; i++ {
		fmt.Scan(&as[i])
	}

	ds := make([]int, n+1)

	cur := 1
	for i := 1; i <= k; i++ {
		cur = as[cur]
		if ds[cur] == 0 {
			ds[cur] = i
			continue
		}

		d := i - ds[cur]
		if d <= k-i {
			i += (k - i) / d * d
		}
	}

	fmt.Println(cur)
}