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<cstdio>
long long n,k,a[500005],f[500005],cnt;
int dfs(int i,int k){
    if(k==0)return i;
    if(!f[i])return f[i]=cnt++,dfs(a[i],k-1);
    else{
        k%=(cnt-f[i]);int ret=i;
        for(int i=1;i<=k;i++)ret=a[ret];
        return ret;
    }
}
int main(){
    scanf("%lld%lld",&n,&k);
    for(int i=1;i<=n;i++)scanf("%lld",a+i);
    printf("%d\n",dfs(1,k));
}