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 (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):   
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz') 
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    class SegTree:
        """
        ref: https://qiita.com/takayg1/items/c811bd07c21923d7ec69
        init(init_val, ide_ele): 配列init_valで初期化 O(N)
        update(k, x): k番目の値をxに更新 O(logN)
        query(l, r): 区間[l, r)をsegfuncしたものを返す O(logN)
        """
        def __init__(self, init_val, segfunc, ide_ele):
            """
            init_val: 配列の初期値
            segfunc: 区間にしたい操作
            ide_ele: 単位元
            n: 要素数
            num: n以上の最小の2のべき乗
            tree: セグメント木(1-index)
            """
            n = len(init_val)
            self.segfunc = segfunc
            self.ide_ele = ide_ele
            self.num = 1 << (n - 1).bit_length()
            self.tree = [ide_ele] * 2 * self.num
            
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            
            for i in range(self.num - 1, 0, -1):
                self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])

        def update(self, k, x):
            """
            k番目の値をxに更新
            k: index(0-index)
            x: update value
            """
            k += self.num
            self.tree[k] = x
            while k > 1:
                self.tree[k >> 1] = self.segfunc(self.tree[k], self.tree[k ^ 1])
                k >>= 1

        def query(self, l, r):
            """
            [l, r)のsegfuncしたものを得る
            l: index(0-index)
            r: index(0-index)
            """
            res = self.ide_ele
            l += self.num
            r += self.num
            while l < r:
                if l & 1:
                    res = self.segfunc(res, self.tree[l])
                    l += 1
                if r & 1:
                    res = self.segfunc(res, self.tree[r - 1])
                l >>= 1
                r >>= 1
            return res

    
    
    
    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        
        
        
        
        
        d = [[float("inf")]*number_vertex for i in range(number_vertex)]
        for x, y, dist in XYD:
            if shift_one_for_vertex:
                x = x - 1
                y = y - 1
            d[x][y] = dist
            d[y][x] = dist
        for i in range(number_vertex):
            d[i][i] = 0 
        for k in range(number_vertex):
            for i in range(number_vertex):
                for j in range(number_vertex):
                    d[i][j] = min(d[i][j],d[i][k] + d[k][j])
        return d


    """ initialize variables and set inputs
    
        
        
            
            
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    r_float = lambda: float(r())
    R = lambda: list(map(int, r().split()))
    R_str = lambda: r().split()
    R_map = lambda: map(int, r().split())
    R_float = lambda: list(map(float, r().split()))
    R_tuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    
    
    N, K = R()
    A = R()
    arrived = [False] * N
    here = 0
    arrived[0] = True
    first_visit = [-1] * N
    visiting = 0
    first_visit[0] = visiting
    while True:
        here = A[here] - 1
        visiting += 1
        if arrived[here]:
            loop_num = visiting - first_visit[here]
            break
        else:
            arrived[here] = True
            first_visit[here] = visiting
    kk = K - first_visit[here] 
    if kk < 0:
        here = 0
        for i in range(K):
            here = A[here] - 1
        print(here+1)
        return
    kkk = kk % loop_num
    for i in range(kkk):
        here = A[here] - 1
    print(here+1)
    
            
        
        
        

        
    
    
    

    
    
    


    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
from collections import defaultdict
N, K = map(int, input().split())
A = list(map(lambda x: int(x)-1, input().split()))
now = 0
counter = defaultdict(int)
counter[now] += 1
roop = []
if 2*N >= K:
    
    now = 0
    for i in range(K):
        now = A[now]
    print(now+1)
    exit()

for i in range(1, K+1):  
    now = A[now]
    counter[now] += 1  
    
    if counter[now] == 2:  
        roop.append(now)  

    if counter[now] == 3:
        tmp = i-1
        now = roop[-1]
        break



print(roop[(K-tmp) % len(roop)-1]+1)

Solution (Python):




geta = lambda fn: list(map(fn, input().split()))

N, K = geta(int)
A = [1] + geta(int)

d = dict()

cur, pos = 0, 0

while cur not in d:
    if pos == K + 1:
        print(cur)
        exit()

    d[cur] = pos
    cur = A[cur]
    pos += 1

l = d[cur] + (K - d[cur] + 1) % (pos - d[cur])

for k in d:
    if d[k] == l:
        print(k)

Solution (Python):
N, K = map(int, input().split())
A = [int(i) for i in input().split()]

count = 0
now = 1
route = []
visited = set([1])
visit_time = [0]*N
visit_time[0] = 0

while True:
    route.append(now)
    old = now
    now = A[now-1]
    count += 1
    if count == K:
        Kth = now
    
    if now in visited:
        break
    else:
        visited.add(now)
        visit_time[now-1] = count

loop_s = now
loop_e = old

num_s = visit_time[loop_s-1]
num_e = visit_time[loop_e-1]

finish = (K-num_s)%(num_e-num_s+1)



if K < num_s:
    print(Kth)
else:
    print(route[finish+num_s])

Solution (Python):
from heapq import heappush, heappop, heapify
from collections import deque, defaultdict, Counter
import itertools
from itertools import permutations, combinations, accumulate, product, combinations_with_replacement
import sys
import bisect
import string
import math
import time


def I(): return int(input())
def S(): return input()
def MI(): return map(int, input().split())
def MS(): return map(str, input().split())
def LI(): return [int(i) for i in input().split()]
def LI_(): return [int(i)-1 for i in input().split()]
def StoI(): return [ord(i)-97 for i in input()]
def ItoS(nn): return chr(nn+97)
def input(): return sys.stdin.readline().rstrip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def print_matrix(mat):
    for i in range(len(mat)):
        print(*['IINF' if v == IINF else "{:0=4}".format(v) for v in mat[i]])


yn = {False: 'No', True: 'Yes'}
YN = {False: 'NO', True: 'YES'}
MOD = 10**9+7
inf = float('inf')
IINF = 10**19
l_alp = string.ascii_lowercase
u_alp = string.ascii_uppercase
ts = time.time()
sys.setrecursionlimit(10**6)
nums = ['1', '2', '3', '4', '5', '6', '7', '8', '9', '10']
show_flg = False


def bfs(graph, initial, MX):
    n = len(graph) - 1
    dist = [-1] * (n + 1)
    q = deque([initial])
    visited = [False] * (n + 1)
    visited[initial] = True
    dist = []

    while len(q) != 0:
        edge = q.popleft()
        nxt = graph[edge]
        dist.append(edge)

        if len(dist) == MX:
            return dist

        for i, e in enumerate(nxt):
            q.append(e)

    return dist


def main():
    N, K = MI()
    A = [i-1 for i in MI()]
    edges = [[] for i in range(N)]
    LIMIT = 3*10**5

    for i in range(N):
        edges[i].append(A[i])

    ret = bfs(edges, 0, LIMIT)
    m = defaultdict(int)
    loop_start = None
    loop_end = None
    for i in range(len(ret)):
        v = ret[i]
        if m[v] == 0:
            m[v] = i
        elif m[v] != 0:
            loop_start = m[v]
            loop_end = i - 1
            break
            
    

    if K <= LIMIT:
        print(ret[K]+1)
    else:
        
        
        
        K -= loop_start
        loop_c = loop_end - loop_start + 1
        n_ret = ret[loop_start:]
        
        print(n_ret[K % loop_c]+1)
        
        
        


if __name__ == '__main__':
    main()

Solution (Python):
N, K = map(int, input().split())
A = [int(x) - 1 for x in input().split()]


loop = 0
city = 0
b = set([0])
while True:
    loop += 1
    if A[city] in b:
        break
    else:
        city = A[city]
        b.add(city)

loop_start = A[city]


pre = 0
city = 0
while True:
    pre += 1
    if A[city] == loop_start:
        break
    else:
        city = A[city]

if loop > pre:
    loop -= pre

if K < pre:  
    city = 0
    for i in range(K):
        city = A[city]
    print(city + 1)
    
else:  
    K -= pre
    last = K % loop
    city = loop_start
    
    for i in range(last):
        city = A[city]
    print(city + 1)

Solution (Python):
def main():
    n,k=map(int,input().split())
    a=list(map(int,input().split()))
    cnt=0
    b=[1]
    res=[-1]*n
    res[0]=0
    flg=0
    now=1
    start=0
    t=1
    while flg==0:
        cnt+=1
        if res[a[now-1]-1]==-1:
            res[a[now-1]-1]=cnt
            b.append(a[now-1])
            now=a[now-1]
        else:
            start=res[a[now-1]-1]
            t=cnt-start
            if cnt<=k:
                flg=1
                k-=start
            else:
                flg=2
    if flg==1:
        print(b[start+(k%t)])
    else:
        print(b[k])
if __name__=="__main__":
    main()

Solution (Python):
N, K = map(int,input().split())
A = list(map(int,input().split()))
A = [A[k]-1 for k in range(N)]
now = 0
for k in range(70):
    if (K>>k)&1 == 1:
        now = A[now]
    A = [A[A[l]] for l in range(N)]
print(now+1)

Solution (Python):
n, k = map(int, input().split())
a = list(map(int, input().split()))
visited = [False for i in range(n)]
town = []

now_town = 0
step = 0
while step <= k:
    visited[now_town] = step
    next_town = a[now_town] - 1
    town.append(now_town)
    if visited[next_town] is False:
        now_town = next_town
        step += 1
    else:
        break

pre_step = visited[next_town]
loop_step = step - pre_step + 1
loop = town[pre_step:(step+1)]
loop.append(town[0])

index = (k - pre_step) % loop_step
ans =loop[index] + 1
print(ans)

Solution (Python):

def main():
  n, k = map(int, input().split())

  A = tuple(map(lambda a: int(a) - 1, input().split()))

  arrival = [None] * n
  arrival[0] = 0

  pos = 0
  for i in range(1, k + 1):
    next_pos = A[pos]

    if arrival[next_pos]:
      loop_len = i - arrival[next_pos]
      remaining = k - i
      kk = arrival[next_pos] + remaining % loop_len
      print(arrival.index(kk) + 1)
      return

    arrival[next_pos] = i
    pos = next_pos

  print(pos + 1)


main()

Solution (Python):
n,k=map(int,input().split())
a=list(map(int,input().split()))
s=1
sa=set()
d=dict()
count=0
niko=0
anss=0
bx=False
while True:
  count+=1
  if count==k:
    anss=a[s-1]
    bx=True
    print(a[s-1])
    count-1
    break
  if not (a[s-1] in sa):
    sa.add(a[s-1])
    d[a[s-1]]=count
    s=a[s-1]
  else:
    niko=a[s-1]
    number=count-d[a[s-1]]
    break
if bx==False:
  lf=False
  ans_list=[]
  kaisu=0
  for i,j in d.items():
    if i==niko:
      lf=True
      kaisu=j
    if lf==True:
      ans_list.append(i)
  print(ans_list[(k-kaisu)%number])

Solution (Python):

MOD = 10 ** 9 + 7
INFI = 10**10

import math

import itertools
import heapq


import copy
from functools import lru_cache

def sosuhante(n):
    for k in range(2, int(math.sqrt(n))+1):
        if n% k ==0:
            return False
    return True
def cmb(n, r):
    if n - r < r: r = n - r
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k in range(r)]

    for p in range(2,r+1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p-1,r,p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot

    result = 1
    for k in range(r):
        if numerator[k] > 1:
            result *= int(numerator[k])

    return result

def kingaku(a,b,n):
    keta=len(str(n))
    return a*n+b*keta

def my_index(l, x, default=False):
    if x in l:
        return l.index(x)
    else:
        return default




def ret(a):
    c=[None]*(len(a)-1)
    if len(a)==1:
        return a[0]
    elif len(a)==0:
        return 0
    for i in range(1,len(a)):
        c[i-1]=abs(a[i]-a[i-1])
    return ret(c)


def main():
    n,k=map(int,input().split())
    a =list(map(int,input().split()))
    town=[-1 for _ in range(n)]
    town[0]=0
    now=0
    for i in range(n):
        if town[a[now]-1]==-1:
            town[a[now]-1]=i+1
            now=a[now]-1
        else:
            sec=a[now]-1
            break

  
    town2 = [-1 for _ in range(n)]
    town2[sec] = 0
    now = sec
    for i in range(n):
        if town2[a[now] - 1] == -1:
            town2[a[now] - 1] = i + 1
            now = a[now] - 1
        else:
            thi = a[now] - 1
            break


    firstloop=max(town)+1
    secondloop=max(town2)+1
    ans=0
    if k<firstloop:
        ans=town.index(k)+1
    else:
        k-=firstloop
        kai=k//secondloop
        k-=kai*secondloop
        ans=town2.index(k)+1
    print(ans)

if __name__ == "__main__":

    main()

Solution (Python):
n,k = map(int, input().split())

A = list(map(int, input().split()))
check_list = [0]*n

pos = 0
loop_left = []
loop = []

while check_list[pos]<2:
  
  if check_list[pos]==0:
    loop_left.append(pos+1) 
    
  if check_list[pos]==1:
    loop.append(pos+1)
  
  check_list[pos] += 1
  pos = A[pos]-1

if k<=len(loop_left)-1:
  print(loop_left[k])
else:
  k -= (len(loop_left)-len(loop))
  ind = k%len(loop)
  print(loop[ind])

Solution (Python):
N, K = list(map(int, input().split()))

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

visited = [False] * N

now = 1


while True:
    if K == 0:
        break
    visited[now-1] = True
    now = A[now-1]
    K -= 1
    if visited[now-1]:
        break


visited2 = [False] * N

while True:
    if K == 0:
        break
    visited2[now-1] = True
    now = A[now-1]
    K -= 1
    if visited2[now-1]:
        break

if K == 0:
    print(now)

else:
    K = K % visited2.count(True)
    while True:
        if K == 0:
            break
        now = A[now-1]
        K -= 1
    print(now)

Solution (Python):

N, K = map(int,input().split())
A = list(map(int,input().split()))
pos = 0
flg = [0] * N
route = [0]
is_ok = 0
while K > 0:
    K-=1
    if flg[pos] == 1 and is_ok==0:
        route = route[route.index(A[pos] - 1):]
        K%=len(route)
        is_ok = 1

    flg[pos] = 1
    pos = A[pos] - 1
    route.append(pos)

print(pos + 1)

Solution (Python):
N,K=map(int,input().split(' '))
A=list(map(lambda x:int(x)-1,input().split(' ')))
roop=[0]
flg = [0 for i in range(N)]
flg[0]=1
n = A[0]
for i in range(2,N+1):
    if flg[n]==0:
        roop.append(n)
        flg[n] = i
        n = A[n]
    else:
        end=i
        break
if K <len(roop):
    print(roop[K]+1)
else:
    K-=flg[n]-1
    K%=(end-flg[n])
    roop=roop[flg[n]-1:end]
    print(roop[K]+1)

Solution (Python):



debug=1
def pront(*n):
    if debug==1:
        print(n)
        


base=10**9+7

def add(a,b):
    return (a+b)%base

def sub(a,b):
    return (a-b)%base

def multi(a,b):
    return (a*b)%base

def exp(a,b):
    x=1
    c=a
    d=b
    while d!=0:
        if d%2==1:
            x=multi(x,c)
        c=(c**2)%base
        d=d//2
    return x

def div(a,b):
    return(multi(a,exp(b,base-2)))


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

A=list(map(int,input().split()))
B=[0 for i in range(len(A))]

x=[]
y={}
i=0
j=1
while True:
    if B[i]!=0:
        p=B[i]
        break
    else:
        B[i]=j
        x.append(A[i])
    i=A[i]-1
    j+=1

T=len(x)-p+1

if K<=p:
    print(x[K-1])
else:
    print(x[((K-p+1)%T)+p-2])

Solution (Python):
n, k = map(int, input().split())
an = list(map(int, input().split())) 

group = [0]
now = 0
seen = [0]*n
seen[0] = 1
while True:
    now = an[now] - 1
    
    group.append(now)
    if seen[now] == 1:
        break
    seen[now] = 1

l = len(group)
a = group.index(group[-1])
roop = l - a - 1
if k < a:
    print(group[k] + 1)
else:
    x = (k - a) % roop
    print(group[a + x] + 1)

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

cnt = [0]*N
town = 1
for i in range(K):
    if cnt[town-1] ==1:
        break

    cnt[town-1] += 1
    town = A[town-1]


ans1 = sum(cnt)

import copy
town2 = copy.deepcopy(town)

cnt2 = [0]*N

for i in range(K):
    if cnt2[town2-1] ==1:
        break

    cnt2[town2-1] += 1
    town2 = A[town2-1]
    
ans2 = sum(cnt2)

if K <= 10**8:
    town4 = 1
    for i in range(K):
        town4 = A[town4-1]
    print(town4)
else:
    town3 = 1
    cnt3=[0]*N
    K2 = ((K-(ans1-ans2))%(ans2))+(ans1-ans2)
    for i in range(K2):
        if cnt3[town3-1] ==1:
            break

        cnt[town3-1] += 1
        town3 = A[town3-1]
    print(town3)

Solution (Python):
N,K=list(map(int,input().split()))
A=list(map(int,input().split()))
B=[0]*(N+1)
counter=1
looper=0
start=0
loopf=0
now=1
A=[0]+A
if N>K:
    for i in range(0,K):
        now=A[now]
    print(now)
    exit()

while True:
    if B[now]==0:
        B[now]=counter
        counter+=1
        now=A[now]
    else:
        start=B[now]
        loopf=now
        looper=counter-start
        break
K=K+1-start
K=K%looper
for i in range(0,K):
    loopf=A[loopf]
print(loopf)

Solution (Python):
n, k = map(int, input().split())
a = list(map(int, input().split()))

flg = True
c = [0 for i in range(n)]
i = 1
b = []
d = []
one = False
while flg:
	x = i-1
	if c[x] == 1 and a[x] == 1:
		flg = False
		one = True
		break
	elif c[x] == 3:
		flg = False
		break
	else:
		c[x] += 1
		if c[x] == 1:
			b.append(x+1)
		if c[x] == 2:
			d.append(x+1)
	i = a[x]
y = k % len(b)
ans = b[y]
if k < len(b):
	print (ans)
else:
	if one:
		print (ans)
	else:
		k -= len(b)
		y = k % len(d)
		ans = d[y]
		print (ans)

Solution (Python):
n,k = map(int,input().split())
a = [-1] + list(map(int,input().split()))
if k < 2*10**5:
    now = 1
    for _ in range(k):
        now = a[now]
    print(now)
    exit()

ispass = [False]*n
now = 1
loop = set()
loop_first = -1
for _ in range(2*n):
    if ispass[now-1] == False:
        ispass[now-1] = True
    else:
        if loop_first == -1:
            loop_first = now
        loop.add(now)
    now = a[now]

k = k - (ispass.count(1) - len(loop))
k = k % len(loop)

now = loop_first
for _ in range(k):
    now = a[now]
print(now)