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>
int n,a[200000],r,t[200000],i;
long long k,q;
int main(){
    scanf("%d%lld",&n,&k);
    for(i=0;i<n;i++){scanf("%d",&a[i]);t[i]=-1;}
    r=1;
    for(i=0;i<200000;i++){
        if(t[r-1]==-1)t[r-1]=i;
        else{
            q=(k-t[r-1])%(i-t[r-1])+t[r-1];
            break;
        }
        r=a[r-1];
    }
    for(i=0;i<200000;i++)if(t[i]==q)break;
    printf("%d",i+1);
    return 0;
}