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



Sample input:
4 5
3 2 4 1


Sample output:
4

Submission status: Accepted

Solution code:
def main(sample_file = ''):

    """ convenient functions
    # for i, a in enumerate(iterable)
    # q, mod = divmod(a, b)
    # divmod(x, y) returns the tuple (x//y, x%y)
    # Higher-order function: reduce(operator.mul, xyz_count, 1)
    # manage median(s) using two heapq https://atcoder.jp/contests/abc127/tasks/abc127_f
    """

    """convenient decorator
    # @functools.lru_cache():
    # to facilitate use of recursive function
        # ex:
        # from functools import lru_cache
        # import sys
        # sys.setrecursionlimit(10**9)
        # @lru_cache(maxsize=None)
        # def fib(n):
        #     if n < 2:
        #         return n
        #     return fib(n-1) + fib(n-2)
        # print(fib(1000))
    """
    
    # import numpy as np
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product # https://docs.python.org/ja/3/library/itertools.html
    # accumulate() returns iterator! to get list: list(accumulate())
    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 = []  # prime factor
        b, e = 2, 0  # base, exponent
        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
        """
        # TODO: How should I do when n - r is negative?
        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 # https://docs.python.org/ja/3/library/collections.html#collections.deque
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest # https://docs.python.org/ja/3/library/heapq.html
    from copy import deepcopy, copy # https://docs.python.org/ja/3/library/copy.html
    import operator
    from operator import itemgetter #sort 
    # ex1: List.sort(key=itemgetter(1))
    # ex2: sorted(tuples, key=itemgetter(1,2))
    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 # Deprecated since version 3.5: Use math.gcd() instead.
    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)
    
    # first create factorial_list
    # fac_list = mod_factorial_list(n)
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    AtoZ = list('abcdefghijklmnopqrsruvwxyz') # 26
    modpow = lambda a, n, p = MOD: pow(a, n, p) # Recursive function in python is slow!
    def modinv(a, p = MOD):
        # evaluate reciprocal using Fermat's little theorem:
        # a**(p-1) is identical to 1 (mod p) when a and p is coprime
        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):
        # fac_list = modfactorial_list(100)
        # print(modcomb(100, 5, modfactorial_list(100)))
        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
            # 配列の値を葉にセット
            for i in range(n):
                self.tree[self.num + i] = init_val[i]
            # 構築していく
            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

    # ************ Graph ************
    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # 最短経路問題: https://ja.wikipedia.org/wiki/%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E5%95%8F%E9%A1%8C
    
    # Bellman-Ford: O(|V||E|). Use this if there exists an edge with negative length in the graph
    # After N steps, the shortest path has converded if there doesn't exist an cycle of edges with negative
    # Watch out: d[N] == d[2*N] doesn't necessarily mean the graph doesn't have negative cycle
    # ref: https://www.youtube.com/watch?v=1Z6ofKN03_Y

    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]

    # Warshall Floyd O(V**3)
    def warshall_floyd(number_vertex, XYD, shift_one_for_vertex=False):
        # ref: https://juppy.hatenablog.com/entry/2018/11/01/%E8%9F%BB%E6%9C%AC_python_%E5%85%A8%E7%82%B9%E5%AF%BE%E6%9C%80%E7%9F%AD%E7%B5%8C%E8%B7%AF%E6%B3%95%EF%BC%88%E3%83%AF%E3%83%BC%E3%82%B7%E3%83%A3%E3%83%AB%E3%83%95%E3%83%AD%E3%82%A4%E3%83%89%E6%B3%95
        # number_vertex: len(vertex)
        # XYD: list of distance from x to y
        # shift_one_for_vertex: XYDの値が1~Nの時(0~N-1でない時)に調整するフラグ。
        # d[i][j]: iからjへの最短距離
        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 # distance of same vertex is 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
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array:
            # ex) [[0] * N for _ in range(N)]
            # ex2) dp = [[0] * (N+1) for _ in range(W*2)]
    # set inputs
        # put inputs between specific values (almost as quickly)
        # ex) S = [-INF] + [int(r()) for _ in range(A)] + [INF]
        # open(0).read() is sometimes useful:
        # ex) n, m, *x = map(int, open(0).read().split())
        #     min(x[::2]) - max(x[1::2])
        # ex2) *x, = map(int, open(0).read().split())
        #     don't forget to add comma after *x if only one variable is used
    # preprocessing
        # transpose = [x for x in zip(*data)]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [(1, 4, 7), (2, 5, 8), (3, 6, 9)]
        # flat = [flatten for inner in data for flatten in inner]
        # ex) [[1, 2, 3], [4, 5, 6], [7, 8, 9]] => [1, 2, 3, 4, 5, 6, 7, 8, 9]
    # calculate and output
        # output pattern
        # ex1) print(*l) => when l = [2, 5, 6], printed 2 5 6
    """

    # functions to read input
    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
    # single int: int(r())
    # single string: r()
    # single float: float(r())
    # line int: R()
    # line string: r().split()
    # line (str, int, int): [j if i == 0 else int(j) for i, j in enumerate(r().split())]
    # lines int: [R() for _ in range(n)]
    """

    # for test
    if sample_file:
        sys.stdin = open(sample_file)
        
    # ----------------------------------
    # main
    #%%
    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)
    
            
        
        
        

        
    
    
    # 小文字をカウントしたリストを持つセグ木で行けそう。

    
    # a = [14, 5, 9, 13, 7, 12, 11, 1, 7, 8]
    


    #%%
    # end of main
    # ----------------------------------

    """memo: how to use defaultdict of list
    # initialize
    Dic = defaultdict(list)
    # append / extend
    Dic[x].append(y)
    # three methods for loop: keys(), values(), items()
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    # to make binary digits text
    >>> a = 5
    >>> bin_str_a = format(a, '#06b')
    >>> print(bin_str_a)
    0b0101 # first 2 strings (='0b') indicates it is binary
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Submission status: Accepted

Solution code:
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:
    # 普通にシミュレーション
    now = 0
    for i in range(K):
        now = A[now]
    print(now+1)
    exit()

for i in range(1, K+1):  # 1回目のテレポート
    now = A[now]
    counter[now] += 1  # その街に訪れたという証拠
    # ここからループが始まる
    if counter[now] == 2:  # 二度目の訪問なら
        roop.append(now)  # 始まりの土地

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


# print((K-tmp) % len(roop))  # 残りのループ回数
print(roop[(K-tmp) % len(roop)-1]+1)

Submission status: Accepted

Solution code:
# import sys
# sys.setrecursionlimit
# from collections import defaultdict

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)

Submission status: Accepted

Solution code:
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
    #print(now, visited)
    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)
#print(route, visit_time, loop_s, loop_e, num_e, num_s)
#print(finish)

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

Submission status: Accepted

Solution code:
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
# show_flg = True

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
            # print(i)
    # print(ret[:5+1])

    if K <= LIMIT:
        print(ret[K]+1)
    else:
        # print(K % loop)
        # print(loop_start, loop_end)
        # org_K = K
        K -= loop_start
        loop_c = loop_end - loop_start + 1
        n_ret = ret[loop_start:]
        # print(n_ret[:15], 'loop_c',loop_c, 'K', K)
        print(n_ret[K % loop_c]+1)
        # print(ret[org_K]+1)
        # print(ret[:10])
        # print(ret[org_K])


if __name__ == '__main__':
    main()

Submission status: Accepted

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

# 最初のループを回るまで
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]

# ループの始点にたどり着くまで
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:  # ループに入る前に終了の場合
    city = 0
    for i in range(K):
        city = A[city]
    print(city + 1)
    
else:  # ループに入って終了
    K -= pre
    last = K % loop
    city = loop_start
    
    for i in range(last):
        city = A[city]
    print(city + 1)

Submission status: Accepted

Solution code:
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()

Submission status: Accepted

Solution code:
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)

Submission status: Accepted

Solution code:
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)

Submission status: Accepted

Solution code:

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()

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
#import sys
MOD = 10 ** 9 + 7
INFI = 10**10
#input = sys.stdin.readline
import math

import itertools
import heapq
#import bisect

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

#    h,w,a,b = map(int, input().split())
#    c = [[0 for j in range(n)] for i in range(n)]

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
#        if i==n-1:
  #          sec=a[now]-1
    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
#    print(town)
#    print(town2)
    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()

Submission status: Accepted

Solution code:
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])

Submission status: Accepted

Solution code:
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)