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: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<stdbool.h>
#include<math.h>
#include<limits.h>
#define MAX 200010
typedef long long ll;
ll N,K;
ll A[MAX];
ll loop_start=0;
ll loop_end=0;
bool bit[MAX]={false};
ll memo[MAX];

void solve(ll town){
    bit[town] = true;
    memo[++loop_end] = town;
    if(bit[A[town]] == true){
        for(ll i=1;i<loop_end;i++){
            if(memo[i] == A[town]){
                loop_start = i;
            }
        }
    }
    else solve(A[town]);
}
int main(){
    scanf("%lld %lld",&N,&K);
    for(ll i=1;i<=N;i++)
        scanf("%lld",A+i);
    solve(1);
    if(K <= loop_start) printf("%lld",memo[K]);
    else
        printf("%lld",memo[loop_start + (K-loop_start+1)%(loop_end-loop_start+1)]);
    return 0;
}