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 Python (3.8.2) (judge verdict: Runtime Error)

n, k = map(int, input().split()) 
a_list = list(map(int, input().split())) 

rireki = [0] * (n+10)
curr_c = 1
rireki[1] = 0

no_loop_count = k
loop_cnt = 1

mugen = False
for i in range(n):
    next_c = a_list[curr_c-1]
    # print(i, curr_c, next_c)
    # if next_c == curr_c:
    #     mugen = True
    if next_c == 1:
        no_loop_count = 0
        loop_cnt = i + 1
        break
    elif rireki[next_c] == 0:
        rireki[next_c] = i+1
    else:
        # print(next_c)
        no_loop_count = rireki[next_c] -1
        loop_cnt = i - no_loop_count
        break
    curr_c = next_c

if loop_cnt ==0:
    loop_cnt = 1

# if not mugen:
if k <= no_loop_count:
    ans = rireki.index(k)
else:
    # print('k',k)
    # print('no', no_loop_count)
    # print('lo', loop_cnt)
    ind = (k-1-no_loop_count)%loop_cnt +1
    rireki_fix = [i-no_loop_count for i in rireki]
    # print(ind, 'ind')
    ans = rireki_fix.index(ind)
    # print(rireki_fix)
    print(ans)