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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int maxx = 2e5 + 7;
int n;
map <int, int> pos;
map <int, bool> vis;
int seq[maxx];
LL k;

int main() {
	scanf("%d %lld", &n , &k);
	for(int i = 1; i <= n; i++) scanf("%d", &pos[i]);
	int nxt = 1;
	int t = -1;
	seq[++t] = nxt;
	int i = 1;
	while(!vis[i]) {
		vis[nxt] = 1; //先打标记
		nxt = pos[i]; //更新nxt
		seq[++t] = nxt;
		i = nxt; //替换
	}
	//seq[t]是第一次重复的数字
	//定位第一次出现时的位置fir
	int x = 0;
	for(int j = 0; j < t; j++) {
		if(seq[j] == seq[t]) {
			x = j;
			break;
		}
	}
	//cout << x << endl;
	if(k <= x) printf("%d\n", seq[k]);
	else { 
		k -= (LL)x;
		LL id = k % ((LL)t - (LL)x);
		printf("%d\n", seq[x + id]);
	}
	return 0;
}