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
	start := 0
	fmt.Scan(&n, &k)
	a := make([]int, n)
	state := make([]int, n)
	tmp := make([]int, 1000000)
	tmp[0] = 0
	loopLength := 0
 
	for i := 0; i < n; i++ {
		fmt.Scan(&a[i])
	}
 
	for i := 0; i < k; i++ {
		start = a[start] - 1
		tmp[i+1] = start
		if state[start] == 1 {
			for j := 0; j < len(tmp); j++ {
				if tmp[j] == start {
					tmp = tmp[j : i+1]
					loopLength = len(tmp)
					break
				}
			}
			fmt.Println(tmp[(k-i-1)%loopLength] + 1)
			return
		} else {
			state[start] = 1
		}
	}
	fmt.Println(start + 1)
}