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):
n, k = map( int, input().split() )
a = [ 0 ] + list( map( int, input().split() ) )

now = 1
visited = [ 1, -1 ] + [ -1 ] * ( n - 1 )
diary = [ -1, 0 ] + [ -1 ] * ( n - 1 )

for i in range( 1, k+1 ):
    now = a[ now ]
    visited[ i ] = now
    if diary[ now ] != -1:
        cycle = i - diary[ now ]
        d = ( k - i ) % cycle
        now = visited[ diary[ now ] + d ]
        break
    else:
        diary[ now ] = i

print( now )

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

def get_loop_num(start, last):
    x = start
    loops = [start]
    for i in range(K):
        x = A[x-1]
        loops.append(x)
        if x == last:
            return loops

loop_check = [False] * N
loop_check[0] = True
x = 1
for i in range(K):
    new_x = A[x-1]
    if loop_check[new_x-1]:
        start = new_x
        last = x
        loops = get_loop_num(start, last)
        l = (K-i-1) % len(loops)
        print(loops[l])
        exit()
    else:
        loop_check[new_x-1] = True
        x = new_x
print(x)

Solution (Python):

import sys

sys.setrecursionlimit(10 ** 8)
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

N, K = map(int, readline().split())
A = [int(x) - 1 for x in readline().split()]
assert len(A) == N


def solve():
    cur = 0
    seen = {0: 0}
    tele = [0]
    loop = []
    loopenter = -1
    while True:
        nxt = A[cur]
        if nxt in seen:
            loopenter = seen[nxt]
            loop = tele[loopenter:]
            break
        seen[nxt] = len(tele)
        tele.append(nxt)
        cur = nxt

    if K < loopenter:
        return tele[K]
    k = (K - loopenter) % len(loop)
    return loop[k]


if __name__ == "__main__":
    print(solve() + 1)

Solution (Python):
import sys,collections as cl,bisect as bs
sys.setrecursionlimit(100000)
input = sys.stdin.readline
mod = 10**9+7
Max = sys.maxsize
def l(): 
    return list(map(int,input().split()))
def m(): 
    return map(int,input().split())
def onem(): 
    return int(input())
def s(x): 
    a = []
    if len(x) == 0:
        return []
    aa = x[0]
    su = 1
    for i in range(len(x)-1):
        if aa != x[i+1]:
            a.append([aa,su])
            aa = x[i+1]
            su = 1
        else:
            su += 1
    a.append([aa,su])
    return a
def jo(x): 
    return " ".join(map(str,x))
def max2(x): 
    return max(map(max,x))
def In(x,a): 
    k = bs.bisect_left(a,x)
    if k != len(a) and a[k] ==  x:
        return True
    else:
        return False

def pow_k(x, n):
    ans = 1
    while n:
        if n % 2:
            ans *= x
        x *= x
        n >>= 1
    return ans

"""
def nibu(x,n,r):
    ll = 0
    rr = r
    while True:
        mid = (ll+rr)//2

    if rr == mid:
        return ll
    if (ここに評価入れる):
        rr = mid
    else:
        ll = mid+1
"""


n,k = m()

a = l()

po = [-1 for i in range(n)]

po[0] = 0
now = 0
for i in range(1,n):
    aaa = a[now]-1
    if po[aaa] == -1:
        po[aaa] = po[now]+1
        now = aaa
    else:
        break

un = po[aaa]
if k <= un:
    for i in range(n):
        if k == po[i]:
            print(i+1)
else:
    k -= un
    mod = po[now]+1 - po[aaa]
    ap = k % mod
    for i in range(n):
        if un + ap == po[i]:
            print(i+1)

Solution (Python):
from collections import defaultdict
n,k = map(int, input().split())
a = list(map(lambda z:int(z)-1, input().split()))
if k <= n:
    now = 0
    for i in range(k):
        now = a[now]
    print(now+1)
    exit()
root = [0]
use = [-1 for _ in range(n)]
use[0] = 0
now = 0
l = -1
for i in range(1,n+1):
    now = a[now]
    if use[now] == -1:
        use[now] = i
    else:
        k -= i
        l = i - use[now]
        break
k %= l
for i in range(k):
    now = a[now]
print(now+1)

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

s = 1
route = []
route.append(s)
arrive = [0]  * N
arrive[s-1] = 1
while True:
    s = A[s-1]
    route.append(s)
    if arrive[s-1] == 1:
        break
    arrive[s-1] = 1


ll = route[-1]
l = len(route)

f = route.index(ll)

if K < f:
    print(route[K])
else:
    roll = route[f::]
    print(roll[(K-f)%(l-1-f)])

Solution (Python):
n,k=map(int,input().split())
a=list(map(int,input().split()))
check=[-1]*n
check[0]=1
ans=[0]
p=0
p=a[p]-1
while check[p]==-1:
  ans.append(p)
  check[p]=1
  p=a[p]-1
ans.append(p)
for i in range(len(ans)-1):
  if ans[i]==ans[-1]:
    x=i
    break
if k<=len(ans):
  print(ans[k]+1)
else:
  print(ans[(k-x)%(len(ans)-1-x)+x]+1)

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

loop = [1]
arrived = [0] * N
now = 1
arrived[now-1] = 1
for i in range(K):
    now = A[now-1]
    if arrived[now-1] == 0:
        arrived[now-1] = 1
        loop.append(now)
    else:
        loop = loop[loop.index(now):]
        arrive = loop[(K-(i+1))%len(loop)]
        print(arrive)
        exit()
print(now)

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

appeared = [False] * N
appeared[0] = True
path = [1]
for _ in range(N+10):
    next_A = As[path[-1] - 1]
    if appeared[next_A-1]:
        break
    else:
        path.append(next_A)
        appeared[next_A-1] = True

before_loop = path.index(next_A)
loop_len = len(path) - before_loop

if K <= before_loop:
    print(path[K])
else:
    print(path[(K - before_loop) % loop_len + before_loop])

Solution (Python):
N,K = [int(hoge) for hoge in input().split()]
A = [int(hoge)-1 for hoge in input().split()]
Went = [False]* N
curpos = 0
Went[0] = True
asiato = [0]
while 1:
    curpos = A[curpos]
    if Went[curpos]:break
    asiato.append(curpos)
    Went[curpos] = True
Loopstart = asiato.index(curpos)
LenLoop = len(asiato) - Loopstart

if K < len(asiato):
    print(asiato[K] + 1)
else:
    X = (K - Loopstart) % LenLoop + Loopstart
    print(asiato[X] + 1)

Solution (Python):
N, K = map(int, input().split())
P = list(map(int, input().split()))
for i in range(N):
    P[i] -= 1
M = 60
step = [[0]*(M+1) for _ in range(N)]

for i in range(N):
    step[i][0] = P[i]

for i in range(1, M+1):
    for j in range(N):
        c = step[j][i-1]
        c = step[c][i-1]
        step[j][i] = c

c = 0
for j in range(M+1):
    if K % 2:
        c = step[c][j]
    K //= 2
print(c+1)

Solution (Python):
import sys, bisect, math, itertools, heapq, collections
from operator import itemgetter

from functools import lru_cache

sys.setrecursionlimit(10**8)
input = sys.stdin.readline
INF = float('inf')
mod = 10**9+7
eps = 10**-7
def inp():
    '''
    一つの整数
    '''
    return int(input())
def inpl():
    '''
    一行に複数の整数
    '''
    return list(map(int, input().split()))

n, k = inpl()
a = inpl()
now = 1
visited = []
visited_set = set()
FLAG=True
for _ in range(k):
    if now in visited_set:
        FLAG=False
        break
    visited_set.add(now)
    visited.append(now)
    now = a[now - 1]
if FLAG:
    print(now)
    exit()
loop_begin = visited.index(now)
k -= loop_begin
loop_len = len(visited) - loop_begin
print(visited[k%loop_len+loop_begin])

Solution (Python):

from collections import defaultdict, deque
from heapq import heappush, heappop
from itertools import permutations, accumulate
import sys
import math
import bisect
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def I(): return int(sys.stdin.readline())
def LS():return [list(x) for x in sys.stdin.readline().split()]
def S():
    res = list(sys.stdin.readline())
    if res[-1] == "\n":
        return res[:-1]
    return res
def IR(n):
    return [I() for i in range(n)]
def LIR(n):
    return [LI() for i in range(n)]
def SR(n):
    return [S() for i in range(n)]
def LSR(n):
    return [LS() for i in range(n)]

sys.setrecursionlimit(1000000)
mod = 1000000007

def solve():
    n,k = LI()
    a = LI()
    for i in range(n):
        a[i] -= 1
    p = [[a[i]] for i in range(n)]
    for i in range(60):
        for x in range(n):
            p[x].append(p[p[x][i]][i])
    x = 0
    while k:
        i = int(math.log(k,2))
        x = p[x][i]
        k -= 1<<i
    print(x+1)
    return


if __name__ == "__main__":
    solve()

Solution (Python):
n, k = map(int, input().split())
a = list(map(int, input().split()))
a = [0] + a

dist = [0] * (n + 1)
cur_dist = 0
cur_pos = 1
while True:
    next_pos = a[cur_pos] 
    cur_dist += 1
    if cur_dist == k:
        print(next_pos)
        exit()
    elif dist[next_pos] == 0:
        dist[next_pos] = cur_dist
        cur_pos = next_pos
    else:
        cycle = cur_dist - dist[next_pos]
        nokori = k - cur_dist
        nokori = nokori % cycle
        cur_pos = next_pos
        for i in range(nokori):
            next_pos = a[cur_pos]
            cur_pos = next_pos
            if i == nokori - 1:
                print(cur_pos)
                exit()

Solution (Python):
n,k = map(int,input().split())
a = list(map(int,input().split()))
l = [1]
al = [0 for i in range(n+1)]
al[1] = 1
now = 1
for i in range(n):
    nex = a[now-1]
    if al[nex] == 0:
        l.append(nex)
        now = nex
        al[nex] += 1
        if i == n-1:
            goal = nex
    else:
        goal = nex
        break
key = 0
count = 0
roop = []
mae = []
for i in l:
    if key == 0:
        if goal == i:
            key = 1
            roop.append(i)
        else:
            mae.append(i)
            count += 1
    else:
        roop.append(i)

if count > k:
    print(mae[k])
else:
    k -= count
    rp = len(roop)
    k %= rp
    print(roop[k])

Solution (Python):
import sys, re, os
from collections import deque, defaultdict, Counter
from math import ceil, sqrt, hypot, factorial, pi, sin, cos, radians, acos, atan, asin, log, log10, gcd
from itertools import permutations, combinations, product, accumulate, combinations_with_replacement
from operator import itemgetter, mul
from copy import deepcopy
from string import ascii_lowercase, ascii_uppercase, digits

def debug(*args):
    if debugmode:
        print(*args)
def input(): return sys.stdin.readline().strip()
def STR(): return input()
def INT(): return int(input())
def FLOAT(): return float(input())
def MAP(): return map(int, input().split())
def S_MAP(): return map(str, input().split())
def LIST(): return list(map(int, input().split()))
def S_LIST(): return list(map(str, input().split()))
def lcm(a, b): return a * b // gcd(a, b)
sys.setrecursionlimit(10 ** 9)
inf = sys.maxsize
mod = 10 ** 9 + 7
dx = [0, 1, 0, -1, 1, -1, -1, 1]
dy = [1, 0, -1, 0, 1, -1, 1, -1]
debugmode = True

n, k = MAP()
a = LIST()
arr = set([])
loop = []
i = 0
idx = 0
cnt = -1
flag = True
flag2 = True
strt = -1
while i < k:
    idx = a[idx] - 1
    i += 1
    l = len(arr)
    arr.add(idx)
    if l == len(arr) and flag:
        flag = False
        cnt = 1
        strt = idx
        loop.append(idx)
    elif not flag and idx == strt:
        flag2 = False
        break
    elif not flag:
        cnt += 1
        loop.append(idx)
    

if flag2:
    print(idx + 1)
else:
    print(loop[(k - i) % cnt] + 1)

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

def getPath():
    curr = 1
    path = [curr]
    seen = {curr}
    while A[curr - 1] not in seen:
        curr = A[curr - 1]
        path.append(curr)
        seen.add(curr)
    assert A[curr - 1] in seen
    index = path.index(A[curr - 1])
    return path[:index], path[index:]

path, cycle = getPath()
if K + 1 < len(path) + len(cycle):
    print((path + cycle)[K])
else:
    print(cycle[(K - len(path)) % len(cycle)])

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

recode = [-1]*N
cnt = 0
current = 0
while True:
    if K <= 0:
        print(current+1)
        break
    if recode[current] == -1:
        recode[current] = cnt
        cnt += 1
        current = A[current]
        K -= 1
    else:
        loop = cnt-recode[current]
        K %= loop
        recode = [-1]*N

Solution (Python):
N,K = map(int,input().split())
A=list(map(lambda x:int(x)-1,input().split()))

loop_start=-1
visited={0}
cur=0
while True:
    cur=A[cur]
    if cur in visited:
        loop_start=cur
        break
    else:
        visited.add(cur)


assert loop_start!=-1


before_loop=0
before_path=[0]
cur=0
while cur!=loop_start:
    cur=A[cur]
    before_loop+=1
    before_path.append(cur)


loop_path=[loop_start]
cur=A[loop_start]
while cur!=loop_start:
    loop_path.append(cur)
    cur=A[cur]



if K>=before_loop:
    K-=before_loop
    print(loop_path[K%len(loop_path)]+1)
else:
    print(before_path[K]+1)

Solution (Python):
n, k = map(int, input().split())
a = list(map(int, input().split()))
for i in range(n): a[i] -= 1
d = [0] * n
nd = [0] * n
r = []
nr = []
i = 0
while True:
    i = a[i]
    if d[i]: break
    d[i] = 1
    r.append(i)
nr.append(i)
nd[i] = 1
while True:
    i = a[i]
    if nd[i]: break
    nd[i] = 1
    nr.append(i)
res = k%len(r)
if len(r) >= k:
    print(r[k-1]+1)
else:
    k -= len(r)
    k %= len(nr)
    print(nr[k-1]+1)

Solution (Python):
N,K=map(int,input().split())
A=list(map(int,input().split()))
x=0
t=0
d=[0]*N
v=[-1]*N
while t==0 or x!=0:
    v[x]=t
    t+=1
    if v[A[x]-1]>=0:
        break
    x=A[x]-1
    d[t]=x
c=t-v[A[x]-1]
print(d[K]+1 if K<t else d[(K-t)%c+v[A[x]-1]]+1)

Solution (Python):
n,k=map(int,input().split())
A=list(map(int,input().split()))
C=[0]
V=[0]*n
V[0]=1
now=0
for i in range(n):
    now=A[now]-1
    if V[now]==1:
        break
    else:
        V[now]=1
        C.append(now)
loop=C.index(now)
L=len(C)-loop
if k>loop:
    print(C[(k-loop)%L+loop]+1)
else:
    print(C[k]+1)

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

order = [-1 for i in range(N)]
order[0] = 0
path = [1]

cnt = 1
before = 1
roop_start = -1
while True:
	nxt = A[before - 1]
	if order[nxt - 1] >= 0:
		roop_start = order[nxt - 1]
		break
	order[nxt - 1] = cnt
	path.append(nxt)
	cnt += 1
	before = nxt

L = len(path)
T = L - roop_start

if K < L:
	print(path[K])
	exit()

K -= roop_start
print(path[roop_start + K % T])

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

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

for i in range(n):
	p[i] -= 1

current_pos = 0
steps = 0
first_occurence = {}

result = -1

while steps < k:
	if current_pos in first_occurence:
		first = first_occurence[current_pos]
		cycle_length = steps - first
		left = (k - steps) % cycle_length
		x = 0
		while x < left:
			current_pos = p[current_pos]
			x += 1

		result = current_pos
		break
	else:
		first_occurence[current_pos] = steps
		steps += 1
		current_pos = p[current_pos]

if result == -1:
	result = current_pos

print(current_pos + 1)

Solution (Python):
import sys; input = sys.stdin.buffer.readline
from collections import defaultdict
con = 10 ** 9 + 7; INF = float("inf")

def getlist():
	return list(map(int, input().split()))


def main():
	N, K = getlist()
	A = getlist()
	if K <= 2 * (10 ** 5):
		loc = 0
		for i in range(K):
			loc = A[loc] - 1
		print(loc + 1)
		return

	loc = 0
	for i in range(2 * (10 ** 5)):
			loc = A[loc] - 1

	start = loc
	loop = [loc]
	loc = A[loc] - 1
	while loc != start:
		loop.append(loc)
		loc = A[loc] - 1

	M = len(loop)
	ans = loop[(K - 2 * (10 ** 5)) % M]
	print(ans + 1)
	
	




if __name__ == '__main__':
	main()

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

if K <= N:
    p = 0
    for i in range(K):
        p = A[p]
    print(p + 1)
    exit()

p = 0
t = [-1] * N
t[0] = 0
for i in range(1, N):
    p = A[p]
    if t[p] != -1:
        break
    t[p] = i

d = i - t[p]
K -= i
K %= d

for i in range(K):
    p = A[p]
print(p + 1)

Solution (Python):
n, k = map(int, input().split())
A = list(map(lambda x: int(x)-1, input().split()))

seen = [0] * n
node = 0
number = 1
while k:
    if seen[node]:
        loop_length = number - seen[node]
        k %= loop_length
        break

    seen[node] = number
    number += 1
    node = A[node]
    k -= 1


for i in range(k):
    node = A[node]

print(node+1)

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

warp = [-1] * (n+1)
warp[1] = 0

now = 1
for i in range(n):
    next_town = a[now-1]
    if warp[next_town] == -1:
        warp[next_town] = i+1
        now = next_town
    else:
        break

loop = (i+1) - warp[next_town]
if warp[next_town] > k:
    count = k
else:
    count = (k-warp[next_town])%loop + warp[next_town]

print(warp.index(count))

Solution (Python):
N,K = map(int,input().split())
A = [-1] + list(map(int,input().split()))

visit = [False for i in range(N+1)]
now = 1
cnt = 0
while True:
    if visit[now]:
        break
    visit[now] = True
    now = A[now]
    cnt += 1
cnt2 = 0
visit2 = [False for i in range(N+1)]
while True:
    if visit2[now]:
        break
    visit2[now] = True
    now = A[now]
    cnt2 += 1

if cnt >= K:
    ans = 1
    for i in range(K):
        ans = A[ans]

else:
    K -= cnt
    K = K%cnt2
    ans = now
    for i in range(K):
        ans = A[ans]
print(ans)

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

for i in range(n):
    a[i] -= 1

l = [-1] * n
l[0] = 0
now = 0

while True:
    nex = a[now]
    if l[nex] != -1:
        lap = l[now] + 1 - l[nex]
        break
    l[nex] = l[now] + 1
    now = nex

if k <= l[now]:
    print(l.index(k) + 1)
else:
    k = l[nex] + (k - l[nex]) % lap
    print(l.index(k) + 1)

Solution (Python):
import sys
readline = sys.stdin.readline

N, K = map(int, readline().split())
A = [a - 1 for a in map(int, readline().split())]

count = 0
a = 0
visited = {0:0}
while True:
    count += 1
    K -= 1
    a = A[a]
    if K == 0:
        print(a + 1)
        exit(0)
    if a in visited:
        T = count - visited[a]
        K = K % T
        break
    else:
        visited[a] = count

for i in range(K):
    a = A[a]

print(a + 1)

Solution (Python):
n,k = map(int, input().split())
a = list(map(int, input().split()))
for i in range(n):
    a[i] -= 1
INF = 1001001001
dist = [INF]*n
dist[0]=0
now=0
flag = True
while 1:
    to = a[now]
    if dist[to]!=INF and flag:
        loop = dist[now] + 1 - dist[to]
        k-=1
        k %= loop
        flag = False
    else:
        dist[to]=dist[now]+1
        k-=1
    now = to
    if k == 0:
        print(to+1)
        break

Solution (Python):
n, k = map(int, input().split())
arr = list(map(int, input().split()))
visited = [-1] * n
visited[0] = 0

i = 0
ptr = 1
while True:
    ptr = arr[ptr-1]
    i += 1
    k -= 1
    if k == 0:
        break
    if visited[ptr-1] != -1:
        k %= i-visited[ptr-1]
    visited[ptr-1] = i
    if k == 0:
        break

print(ptr)

Solution (Python):
(N, K) = [int(n) for n in input().split()]
A = [int(n)-1 for n in input().split()]
v = [-1 for _ in range(N)]

D = [0]
v[0] = 0

cur = A[0]
i = 1

while v[cur] == -1:
    D.append(cur)
    v[cur] = i
    if i == K:
        print(cur+1)
        exit()

    i += 1
    cur = A[cur]

K -= v[cur]
K %= (i - v[cur])

print(D[v[cur] + K]+1)

Solution (Python):
N, K = map(int, input().split())
tele = list(map(int, input().split()))
times = [0] * N
t = 0
pos = 0
looped = False
while K > 0:
    t += 1
    K -= 1
    if times[pos] == 0:
        times[pos] = t
    elif not looped:
        K %= t - times[pos]
        looped = True
    pos = tele[pos] - 1
print(pos + 1)

Solution (Python):
import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

n,k = map(int,input().split())
A = list(map(int,input().split()))
for i in range(n):A[i] -= 1
visited = [-1] * n
visited[0] = 0
now = 0
count = 0
while True:
  now = A[now]
  count += 1
  if count == k:
    print(now+1)
    exit()
  if visited[now] == -1:
    visited[now] = count
  else:
    rooplen = count-visited[now]
    k -= visited[now]
    k = k % rooplen
    break
  

visited = [-1] * n
count = 0
while True:
  
  if count == k:
    print(now+1)
    exit()
  if visited[now] == -1:
    visited[now] = count
  now = A[now]
  count += 1

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

history = [None] * N

pos = 0
for idx in range(N + 1):
    if history[pos] != None:
        offset = history[pos]
        step = idx - offset
        break
    else:
        history[pos] = idx
        pos = A[pos] - 1

if K >= offset:
    n_step = (K - offset) // step
    n_targ = K - (offset + n_step * step)
    for _ in range(n_targ):
        pos = A[pos] - 1
else:
    pos = 0
    for _ in range(K):
        pos = A[pos] - 1
        
print(pos + 1)

Solution (Python):
N,K=list(map(int,input().split()))
A=list(map(int,input().split()))
next_town=1
_vt=[1]
visited_town={1:0}
for i in range(K):
  now_town=next_town
  next_town=A[now_town-1]
  if next_town in visited_town:
    i_town=_vt.index(next_town)
    K-=i_town
    _vt=_vt[i_town:]
    goal=K % len(_vt)
    print(_vt[goal])
    break
  else:
    _vt.append(next_town)
    visited_town[next_town]=0
else:
  print(next_town)

Solution (Python):
def main():
    N, K = map(int, input().split())
    A = list(map(int, input().split()))
    A = [i-1 for i in A]
    l = []
    v = set()
    t = 0
    while True:
        l.append(t)
        if t in v:
            break
        v.add(t)
        t = A[t]
    ll = len(l) - 1 - l.index(t)
    loop = l[l.index(t):-1]
    s = l.index(t)
    if K < len(l):
        return l[K] + 1
    K -= s
    K %= ll
    return loop[K] + 1
print(main())

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

lastVisit = [None] * N
now = 0
n = 0
while lastVisit[now] is None:
    lastVisit[now] = n
    now = As[now]-1
    n += 1
    if n == K:
        print(now+1)
        exit()

for _ in range((K-lastVisit[now]) % (n-lastVisit[now])):
    now = As[now]-1
print(now+1)

Solution (Python):

import sys
sys.setrecursionlimit(10**9)
INF=10**18
MOD=10**9+7
input=lambda: sys.stdin.readline().rstrip()
YesNo=lambda b: bool([print('Yes')] if b else print('No'))
YESNO=lambda b: bool([print('YES')] if b else print('NO'))
int1=lambda x:int(x)-1

def main():
    N,K=map(int,input().split())
    A=tuple(map(int1,input().split()))
    used=[False]*N
    v=0
    while True:
        if used[v]==True:
            loopstart=v
            break
        else:
            used[v]=True
        v=A[v]
    v=0
    d0=-1
    for i in range(10**7):
        if v==loopstart and d0==-1:
            d0=i
        elif v==loopstart and d0!=-1:
            d1=i-d0
            break
        v=A[v]
    K-=d0
    if K>0:
        K-=K//d1*d1
    K+=d0
    v=0
    for _ in range(K):
        v=A[v]
    print(v+1)

if __name__ == '__main__':
    main()

Solution (Python):


def LI():
    return list(map(int, input().split()))


N, K = LI()
A = LI()


def main():
    n = 0
    x = 1
    visit = [None] * N
    while visit[x - 1] is None:
        if n == K:
            print(x)
            return
        visit[x - 1] = n
        n += 1
        x = A[x - 1]
    
    v = n - visit[x - 1]
    s = (K - n) % v
    ans = visit.index(visit[x - 1] + s) + 1
    print(ans)


if __name__ == "__main__":
    main()

Solution (Python):


import sys
read = sys.stdin.read
readline = sys.stdin.readline 


n,k,*a = list(map(int,read().split()))
for i in range(n): a[i] -= 1


now = 0
cnt = 0
used = [-1]*n

while used[now] == -1:
    used[now] = cnt
    cnt += 1
    now = a[now]
    if cnt == k:
        print(now+1)
        exit()

c = cnt - used[now]


k -= used[now]
k %= c
print(used.index(k+used[now])+1)

Solution (Python):
n,k = map(int, input().split())
arr = list(map(int, input().split()))
i = 1
n = 0
visited = {i:n}
while k > 0:
  n += 1
  k -= 1
  i = arr[i-1]
  if i in visited:
    break
  visited[i] = n

if k == 0:
  print(i)
else:
  k %= n-visited[i]
  while k > 0:
    k -= 1
    i = arr[i-1]
  print(i)

Solution (Python):
def main():

    import sys, math
    
    
    from collections import defaultdict as dd, deque
    def data(): return sys.stdin.readline().strip()
    def mdata(): return list(map(int, data().split()))
    def out(*var, end="\n"): sys.stdout.write(' '.join(map(str, var))+end)
    
    INF = int(1e9)
    mod = int(1e9)+7

    n,k=mdata()
    A=mdata()
    cnt=1
    d=dd(int)
    d1=dd(int)
    d[0]=1
    d1[1]=0
    t=0
    while True:
        if d[A[t]-1]==0:
            cnt+=1
            d[A[t]-1]=cnt
            d1[cnt]=A[t]-1
        else:
            ind1=d[A[t]-1]
            ind2=d[t]
            break
        t=A[t]-1
    if k+1<=ind1:
        print(d1[k+1]+1)
    else:
        k+=1
        k-=ind1
        k=k%(ind2-ind1+1)
        print(d1[(ind1+k)]+1)

if __name__ == '__main__':
    main()

Solution (Python):
def main():
    n, k = map(int, input().split())
    a = list(map(int, input().split()))
    f = [True]*n
    cnt = 0
    ans = -1
    x = 0
    while f[x]:
        f[x] = False
        cnt += 1
        x = a[x] - 1
        if cnt == k:
            ans = x+1
            break
    if ans != -1:
        print(ans)
    else:
        k -= cnt
        y = a[x] - 1
        tmp = [x]
        while y != x:
            tmp.append(y)
            y = a[y] - 1
        print(tmp[k%(len(tmp))] + 1)

if __name__ == "__main__":
    main()

Solution (Python):






import sys
input = sys.stdin.readline

import math
from collections import deque
from fractions import gcd
from functools import lru_cache






MOD = 10**9+7
INF = float('inf')






def inputI(): return int(input().strip())
def inputS(): return input().strip()
def inputIL(): return list(map(int,input().split()))
def inputSL(): return list(map(str,input().split()))
def inputILs(n): return list(int(input()) for _ in range(n))
def inputSLs(n): return list(input().strip() for _ in range(n))
def inputILL(n): return [list(map(int, input().split())) for _ in range(n)]
def inputSLL(n): return [list(map(str, input().split())) for _ in range(n)]


def inv(n): return pow(n, MOD-2, MOD)


kaijo_memo = []
def kaijo(n):
  if(len(kaijo_memo) > n):
    return kaijo_memo[n]
  if(len(kaijo_memo) == 0):
    kaijo_memo.append(1)
  while(len(kaijo_memo) <= n):
    kaijo_memo.append(kaijo_memo[-1] * len(kaijo_memo) % MOD)
  return kaijo_memo[n]

gyaku_kaijo_memo = []
def gyaku_kaijo(n):
  if(len(gyaku_kaijo_memo) > n):
    return gyaku_kaijo_memo[n]
  if(len(gyaku_kaijo_memo) == 0):
    gyaku_kaijo_memo.append(1)
  while(len(gyaku_kaijo_memo) <= n):
    gyaku_kaijo_memo.append(gyaku_kaijo_memo[-1] * pow(len(gyaku_kaijo_memo),MOD-2,MOD) % MOD)
  return gyaku_kaijo_memo[n]

def nCr(n,r):
  if(n == r):
    return 1
  if(n < r or r < 0):
    return 0
  ret = 1
  ret = ret * kaijo(n) % MOD
  ret = ret * gyaku_kaijo(r) % MOD
  ret = ret * gyaku_kaijo(n-r) % MOD
  return ret


def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5//1))+1):
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])
    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])
    return arr


def lcm(a, b):
    return a * b // gcd (a, b)





N,K = inputIL()
A = inputIL()

flag = [False for i in range(N)]
route = [0]

now = 0
flag[0] = True
while True:
  n = A[now]-1
  if flag[n] == True:
    loop_point = n
    break
  route.append(n)
  flag[n] = True
  now = n

p = route.index(loop_point)
path = route[:p]
loop = route[p:]

if K <= len(path)-1:
  print(path[K]+1)
else:
  k = K-len(path)
  k = k%len(loop)
  print(loop[k]+1)

Solution (Python):
from collections import defaultdict as dd

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


res = 1
dic=dd(int)

now = 1
mita = set()
mita.add(now)
dic[now] = 1
start = 0
end = 0

while 1:
    next_town = a[now-1]
    
    if next_town in mita:
        start = next_town
        end = now
        break
    else:
        res += 1
        now = next_town
        mita.add(next_town)
        dic[next_town] = res
    if res == K+1:
        print(next_town)
        exit()


loop_num = dic[end] - dic[start] + 1
Kmod = (K-res)%loop_num

now = next_town
for i in range(Kmod):
    next_town = a[now-1]
    now = next_town
print(now)

Solution (Python):
def main():

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

    visited = dict()
    visited[1] = 0
    inv_d = dict()
    inv_d[0] = 1
    j = 0
    period = 0
    shift = 0
    for i in range(1, N+1):
        if A[j] in visited:
            period = i-visited[A[j]]
            shift = visited[A[j]]
            break
        else:
            visited[A[j]] = i
            inv_d[i] = A[j]
            j = A[j]-1

    if K <= shift:
        return inv_d[K]
    else:
        return inv_d[(K-shift) % period + shift]



if __name__ == '__main__':
    print(main())

Solution (Python):
n, k = map(int, input().split())
a = list(map(int, input().split()))
a = [item - 1 for item in a]

current_town = 0
if k < 200000:
    for i in range(k):
        current_town = a[current_town]
    print(current_town + 1)

else:
    passed = [-1] * n
    passed[0] = 0 
    for i in range(1, 1000000):
        current_town = a[current_town]
        if passed[current_town] > -1:
            start = passed[current_town]
            period = i - start
            break
        else:
            passed[current_town] = i

    m = (k - start) % period
    for i in range(m):
        current_town = a[current_town]

    print(current_town + 1)

Solution (Python):
N, K = map(int, input().split())
Alist = list(map(int, input().split()))
path = [0]
next = Alist[0]
seen = set()
seen.add(0)
while (next-1) not in seen:
    seen.add(next-1)
    path.append(next-1)
    next = Alist[next-1]
base = path.index(next-1)
loop_length = len(path) - base
loop = path[base:base+loop_length+1]


if K <= base:
    print(path[K]+1)
else:
    K -= base
    print(loop[K%loop_length]+1)

Solution (Python):
def main():
    import sys
    input = sys.stdin.readline
    N, K = map(int, input().split())
    *A, = map(lambda x: int(x) - 1, input().split())

    P = []
    t = 0
    for i in range(N + 1):
        P.append(t)
        t = A[t]

    t1 = t2 = 0
    t = 0
    first_visit = [-1] * N
    while t <= N:
        town = P[t]
        if first_visit[town] < 0:
            first_visit[town] = t
        else:
            t1 = first_visit[town]
            t2 = t
            break
        t += 1

    term = t2 - t1
    cycle = (K - t1) // term if K >= t1 else 0
    rest = K - term * cycle - t1 if K >= t1 else 0
    ans = P[t1] if K >= t1 else P[K]
    for i in range(rest):
        ans = A[ans]
    print(ans + 1)


if __name__ == '__main__':
    main()