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: Runtime Error)

package main

import (
	"fmt"
)

func main() {
	var N, K int
	fmt.Scanf("%d %d", &N, &K)
	A := make([]int, N)
	for i := 0; i < N; i++ {
		fmt.Scanf("%d", &A[i])
	}

	next := A[0]
	pattern := []int{1}
	counter := make([]int, N)
	for i := 0; i < N; i++ {
		counter[i] = 0
	}
	counter[0]++
	for {
		pattern = append(pattern, next)
		counter[next-1]++
		if counter[next-1] > 1 {
			break
		}
		next = A[next-1]
	}
	patternFastIndex := next
	var patternA, patternB []int
	if patternFastIndex == 1 {
		patternA = pattern[:patternFastIndex-1]
		patternB = pattern[patternFastIndex-1 : len(pattern)-1]
	} else {
		patternA = pattern[:patternFastIndex]
		patternB = pattern[patternFastIndex : len(pattern)-1]
	}
	if K >= len(patternA) {
		fmt.Println(patternB[(K-len(patternA))%len(patternB)])
	} else {
		fmt.Println(patternA[K%len(patternA)])
	}
}