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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

N, K = map(int, input().split())
A = list(map(int, input().split()))

isPassed = [False] * N
town = 0
#2度同じところに行きつくまで繰り返し、ループの枝元探す
while True:
    if isPassed[town]==False:
        isPassed[town] = True
        town = A[town]-1
    else:
        loopPoint = town
        break

#ループまでの長さを測る
onewayLen = 0
town = 0
while town!=loopPoint:
    town = A[town]-1
    onewayLen += 1

#ループ自体の長さを測る
loopLen = 1
town = A[loopPoint] - 1
while town!=loopPoint:
    town = A[town]-1
    loopLen += 1

#解
if K <= onewayLen:
    town = 0
    for i in range(K):
        town = A[town]-1
    print(town)
else:
    loopMod = (K-onewayLen) % loopLen
    town = loopPoint
    for i in range(loopMod):
        town = A[town]-1
    print(town+1)