Problem:


Score : 700 points

Problem Statement

We have a sequence of N \times K integers: X=(X_0,X_1,\cdots,X_{N \times K-1}).
Its elements are represented by another sequence of N integers: A=(A_0,A_1,\cdots,A_{N-1}). For each pair i, j (0 \leq i \leq K-1,\ 0 \leq j \leq N-1), X_{i \times N + j}=A_j holds.

Snuke has an integer sequence s, which is initially empty.
For each i=0,1,2,\cdots,N \times K-1, in this order, he will perform the following operation:

If s does not contain X_i: add X_i to the end of s.

If s does contain X_i: repeatedly delete the element at the end of s until s no longer contains X_i. Note that, in this case, we do not add X_i to the end of s.

Find the elements of s after Snuke finished the operations.

Constraints

1 \leq N \leq 2 \times 10^5

1 \leq K \leq 10^{12}

1 \leq A_i \leq 2 \times 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
A_0 A_1 \cdots A_{N-1}

Output

Print the elements of s after Snuke finished the operations, in order from beginning to end, with spaces in between.

Sample Input 1

3 2
1 2 3

Sample Output 1

2 3

In this case, X=(1,2,3,1,2,3).
We will perform the operations as follows:

i=0: s does not contain 1, so we add 1 to the end of s, resulting in s=(1).

i=1: s does not contain 2, so we add 2 to the end of s, resulting in s=(1,2).

i=2: s does not contain 3, so we add 3 to the end of s, resulting in s=(1,2,3).

i=3: s does contain 1, so we repeatedly delete the element at the end of s as long as s contains 1, which causes the following changes to s: (1,2,3)→(1,2)→(1)→().

i=4: s does not contain 2, so we add 2 to the end of s, resulting in s=(2).

i=5: s does not contain 3, so we add 3 to the end of s, resulting in s=(2,3).

Sample Input 2

5 10
1 2 3 2 3

Sample Output 2

3

Sample Input 3

6 1000000000000
1 1 2 2 3 3

Sample Output 3

s may be empty in the end.

Sample Input 4

11 97
3 1 4 1 5 9 2 6 5 3 5

Sample Output 4

9 2 6



Sample input:
3 2
1 2 3


Sample output:
2 3

Submission status: Wrong Answer

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
    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]

    # Graph: https://en.wikipedia.org/wiki/Directed_graph
    # 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]

    """ initialize variables and set inputs
    # initialize variables
        # to initialize list, use [0] * n
        # to initialize two dimentional array, use [[0] * N for _ in range(N)]
    # 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 = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = 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()
    dbl = [[0] * N for _ in range(42)]
    pre_num = dict()
    first_num = dict()
    for i, a in enumerate(A):
        if a not in pre_num.keys():
            first_num[a] = i
            pre_num[a] = i
        else:
            dbl[0][pre_num[a]] = (i + 1)%N
            pre_num[a] = i
    for a in pre_num.keys():
        dbl[0][pre_num[a]] = (first_num[a] + 1)%N
    # if not next page
    dbl2 = deepcopy(dbl[0])
    for i in range(N-1, -1, -1):
        if dbl[0][i] >= i + 2:
            dbl[0][i] = dbl[0][dbl[0][i]]

    for i in range(1, 42):
        for j in range(N):
            dbl[i][j] = dbl[i-1][dbl[i-1][j]]
    
    bin_str_K = format(K-1, '#42b')
    idx = 0
    for i, digit in enumerate(bin_str_K):
        if digit == '1':
            idx = dbl[42-i-1][idx]
    
    while first_num[A[idx]] + 1 != dbl2[idx] and dbl2[idx] > idx:
        idx = dbl2[idx]
    
    ans = []
    while idx < N:
        if (first_num[A[idx]] + 1)%N == dbl2[idx]:
            ans.append(A[idx])
            idx += 1
        else:
            idx = dbl2[idx]
            if idx == 0:
                break
    
    print(*ans)
    

    # to finish code, use return instead of exit()
    # 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: Wrong Answer

Solution code:
import copy

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

while True :
  cycle.append(copy.deepcopy(list))
  count = count + 1
    
  for i in range(len(a)) :
    if list.count(a[i]) == 0 :
  	  list.append(a[i])
    else :
      list = list[0:list.index(a[i])]
           
  if len(list) == 0 :
    break
       
print(cycle[k % count])

Submission status: Wrong Answer

Solution code:
import sys,heapq
from collections import deque,defaultdict
printn = lambda x: sys.stdout.write(x)
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
DBG = True  and False
def ddprint(x):
  if DBG:
    print(x)

n,k = inm()
a = inl()
nxt = [0]*(2*n)
first = [-1]*n
prev = {}
for i in range(2*n):
    x = a[i%n]
    if x in prev:
        nxt[prev[x]] = i
    prev[x] = i

ddprint(nxt)
#print("hoge")
#exit()  #- no RE.  i.e. RE after here


loopfound = False
i=0
first[0] = 0
while True:
    i0 = i%n
    j = nxt[i0]+1
    nxtj = j + i - i0
    ddprint("  i {} j {} nxtj {} aj0 {}".format(i,j,nxtj,a[j%n]))
    if nxtj >= n*k:
        break
    j0 = j%n
    if first[j0] != -1:
        loopfound = True
        break
    first[j0] = nxtj
    i = nxtj

print("bar")
exit()  # still RE.  i.e. RE before here

ddprint(first)
ddprint("nxtj {} j0 {} lpfd {}".format(nxtj,j0,loopfound))

if loopfound:
    dif = nxtj - first[j0]
    if dif<=0:  # NTBR
        print("foo")
        exit()
    i = nxtj + ((n*k - nxtj) // dif) * dif
    ddprint("nxt {} j0 {} dif {} i {}".format(nxtj,j0,dif,i))
    while True:
        i0 = i%n
        j = nxt[i0] + 1
        nxtj = j+i-i0
        if nxtj >= n*k:
            break
        i = nxtj

ddprint(i)

done = [False] * 200001
stk = []
for j in range(i,n*k):
    ddprint(j)
    ddprint(stk)
    ddprint(done[:11])
    j0 = j%n
    if done[a[j0]]:
        ddprint(a[j0])
        m = len(stk)
        for k in range(m-1,-1,-1):
            x = stk[k]
            ddprint(x)
            stk.pop()
            done[x] = False
            if x==a[j0]:
                break
    else:
        stk.append(a[j0])
        done[a[j0]] = True

for i in stk:
    printn(str(i) + ' ')
print("")

Submission status: Wrong Answer

Solution code:
import sys,heapq
from collections import deque,defaultdict
printn = lambda x: sys.stdout.write(x)
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
DBG = True  and False
def ddprint(x):
  if DBG:
    print(x)

n,k = inm()
a = inl()
nxt = [0]*(2*n)
first = [-1]*n
prev = {}
for i in range(2*n):
    x = a[i%n]
    if x in prev:
        nxt[prev[x]] = i
    prev[x] = i

ddprint(nxt)
#print("hoge")
#exit()  #- no RE.  i.e. RE after here


loopfound = False
i=0
first[0] = 0
while True:
    i0 = i%n
    j = nxt[i0]+1
    nxtj = j + i - i0
    #ddprint("  i {} j {} nxtj {} aj0 {}".format(i,j,nxtj,a[j%n]))
    if nxtj >= n*k:
        break
    j0 = j%n
    if first[j0] != -1:
        loopfound = True
        break
    first[j0] = nxtj
    i = nxtj

print("bar")
exit()  # still RE.  i.e. RE before here

ddprint(first)
ddprint("nxtj {} j0 {} lpfd {}".format(nxtj,j0,loopfound))

if loopfound:
    dif = nxtj - first[j0]
    if dif<=0:  # NTBR
        print("foo")
        exit()
    i = nxtj + ((n*k - nxtj) // dif) * dif
    ddprint("nxt {} j0 {} dif {} i {}".format(nxtj,j0,dif,i))
    while True:
        i0 = i%n
        j = nxt[i0] + 1
        nxtj = j+i-i0
        if nxtj >= n*k:
            break
        i = nxtj

ddprint(i)

done = [False] * 200001
stk = []
for j in range(i,n*k):
    ddprint(j)
    ddprint(stk)
    ddprint(done[:11])
    j0 = j%n
    if done[a[j0]]:
        ddprint(a[j0])
        m = len(stk)
        for k in range(m-1,-1,-1):
            x = stk[k]
            ddprint(x)
            stk.pop()
            done[x] = False
            if x==a[j0]:
                break
    else:
        stk.append(a[j0])
        done[a[j0]] = True

for i in stk:
    printn(str(i) + ' ')
print("")

Submission status: Wrong Answer

Solution code:
import sys,heapq
from collections import deque,defaultdict
printn = lambda x: sys.stdout.write(x)
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
DBG = True  and False
def ddprint(x):
  if DBG:
    print(x)

n,k = inm()
a = inl()
nxt = [0]*(2*n)
first = [-1]*n
prev = {}
for i in range(2*n):
    x = a[i%n]
    if x in prev:
        nxt[prev[x]] = i
    prev[x] = i

ddprint(nxt)
print("hoge")
exit()  #- still RE.  i.e. RE before here


loopfound = False
i=0
first[0] = 0
while True:
    i0 = i%n
    j = nxt[i0]+1
    nxtj = j + i - i0
    ddprint("  i {} j {} nxtj {} aj0 {}".format(i,j,nxtj,a[j%n]))
    if nxtj >= n*k:
        break
    j0 = j%n
    if first[j0] != -1:
        loopfound = True
        break
    first[j0] = nxtj
    i = nxtj

ddprint(first)
ddprint("nxtj {} j0 {} lpfd {}".format(nxtj,j0,loopfound))
#print("bar")
#exit()  - still RE.  i.e. RE before here

if loopfound:
    dif = nxtj - first[j0]
    if dif<=0:  # NTBR
        print("foo")
        exit()
    i = nxtj + ((n*k - nxtj) // dif) * dif
    ddprint("nxt {} j0 {} dif {} i {}".format(nxtj,j0,dif,i))
    while True:
        i0 = i%n
        j = nxt[i0] + 1
        nxtj = j+i-i0
        if nxtj >= n*k:
            break
        i = nxtj

ddprint(i)

done = [False] * 200001
stk = []
for j in range(i,n*k):
    ddprint(j)
    ddprint(stk)
    ddprint(done[:11])
    j0 = j%n
    if done[a[j0]]:
        ddprint(a[j0])
        m = len(stk)
        for k in range(m-1,-1,-1):
            x = stk[k]
            ddprint(x)
            stk.pop()
            done[x] = False
            if x==a[j0]:
                break
    else:
        stk.append(a[j0])
        done[a[j0]] = True

for i in stk:
    printn(str(i) + ' ')
print("")

Submission status: Wrong Answer

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

jumpTable = {}
last_visit = {}
stack = []
i = 0
T = N * K + 1
while i < N * K:
    ind = i % N
    if(A[ind] in stack):
        end = stack.index(A[ind])
        stack = stack[:end]
        jumpTable[last_visit[A[ind]]] = i + 1 - last_visit[A[ind]]
        i += 1
    else:
        stack.append(A[ind])
        last_visit[A[ind]] = i
        i += 1
    if len(stack) == 0 and i % N == 0:
        T = i
        break

remain = N * K % T
i = 0
ret = []
while i < remain:
    ind = i % N
    if A[ind] in ret:
        end = ret.index(A[ind])
        ret = ret[:end]
        i += 1
    if ind in jumpTable:
        i += jumpTable[ind]
    else:
        ret.append(A[ind])
        i += 1

ans = ''
for i in range(len(ret)):
    ans += str(ret[i]) + ' '
print(ans)

Submission status: Wrong Answer

Solution code:
n, k = map(int, input().split())
a = list(map(int, input().split()))
s = []
for i in a:
  if i in s:
    while i != s.pop(-1):
      break
  else:
    s.append(str(i))
print(" ".join(s))

Submission status: Wrong Answer

Solution code:
import math

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

    M=N*K

    logNK=math.floor(math.log2(N*K))
    if logNK==0 :
        logNK=1
    f=([[0]*N for i in range(logNK)])

    #calc f0(n)
    idx=[[] for i in range(200001)]
    for i, a in enumerate(A):
        idx[a].append(i)


    for i, a in enumerate(A):
        l=idx[a]
        n=l.index(i)
        if n+1 == len(l):
            j = N + l[0]
        else:
            j = l[n+1]
        f[0][i]=j-i+1


    for k in range(1,logNK):
        for i in range(N):
            f[k][i]=f[k-1][ i ] + f[ k-1 ][(i + f[k-1][i])%N ]

    #step2
    n=0
    for k in range(logNK-1,0,-1):
        i=n%N
        if n + f[k][i] < M:
            n+=f[k][i]

    print("n=",n)
    print("N*K-n",M-n)
    #step3
    tmp=[]
    for i in range(M-n-1,N):
        imodn=i%N
        if A[imodn] in tmp:
            tmp=tmp[0:tmp.index(A[imodn])]
        else:
            tmp.append(A[imodn])

    print(' '.join(map(str,tmp)))

main()

Submission status: Wrong Answer

Solution code:
import math

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

M=N*K

logNK=math.floor(math.log2(N*K))
if logNK==0 :
    logNK=1
f=([[0]*N for i in range(logNK)])

#calc f0(n)
idx=[[] for i in range(200001)]
for i, a in enumerate(A):
    idx[a].append(i)


for i, a in enumerate(A):
    l=idx[a]
    n=l.index(i)
    if n+1 == len(l):
        j = N + l[0]
    else:
        j = l[n+1]
    f[0][i]=j-i+1


for k in range(1,logNK):
    for i in range(N):
        f[k][i]=f[k-1][ i ] + f[ k-1 ][(i + f[k-1][i])%N ]

#step2
n=0
for k in range(logNK-1,0,-1):
    i=n%N
    if n + f[k][i] < M:
        n+=f[k][i]
"""
#step3
tmp=[]
for i in range(n,M):
    imodn=i%N
    if A[imodn] in tmp:
        tmp=tmp[0:tmp.index(A[imodn])]
    else:
        tmp.append(A[imodn])

print(' '.join(map(str,tmp)))
"""

Submission status: Wrong Answer

Solution code:
import math

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

M=N*K

A2=A*2

logNK=math.floor(math.log2(N*K))
f=([[0]*N for i in range(logNK)])

Submission status: Wrong Answer

Solution code:
N, K = map(int, input().split())
As = list(map(int, input().split()))
M = [[] for i in range(200001)]
for i, a in enumerate(As):
  M[a].append(i)
S = []
for i, a in enumerate(As):
  l = M[a]
  index = l.index(i)
  if index+1 == len(l):
    n = l[0]+N
  else:
    n = l[index+1]
  S.append(n+1-i)
#print(S)
p = 0
while True:
  p = p+S[p%N]
  if p%N == 0:
    break
count = p//N
#print(count)
K = K%count
#print(K)
p = 0
while True:
  q = p+S[p%N]
  if p > N*K:
    break
  p = q
index = p%N
s = []
for a in As[index-1:]:
  i = -1
  for j in range(len(s)):
    if s[j] == a:
      i = j
  if i < 0:
    s.append(a)
  else:
    s = s[0:i]
print(" ".join(map(str, s)))

Submission status: Wrong Answer

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

last = dict()
v = [-1] * N

for i, a in enumerate(A + A) :
    if a in last :
        if last[a] < N :
            v[last[a]] = i + 1
    
    last[a] = i

dist = [-1] * N
cur = 0
s = 0
while dist[cur] < 0 :
    dist[cur] = s 
    s += v[cur] - cur
    cur = v[cur] % N

# d1 - ループに入るまでの長さ, d2 - ループの長さ
d1 = dist[cur]
d2 = s - d1
NK = N * K

if NK > d1 :
    m = (NK-d1) % d2
    s = 0
    while m > dist[cur] - d1 :
        s = dist[cur] - d1
        cur = v[cur] % N
    m -= s
else :
    m = 0
  
ret = []
last = dict()
for a in A[-m:] :
    if a in last and last[a] >= 0 :
        ret = ret[:last[a]]
        last[a] = -1
    else :
        ret.append(a)
        last[a] = len(ret)-1
        
print(' '.join([str(i) for i in ret]))

Submission status: Wrong Answer

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

last = dict()
v = [-1] * N

for i, a in enumerate(A + A) :
    if a in last :
        if last[a] < N :
            v[last[a]] = i + 1
    
    last[a] = i

dist = [-1] * N
cur = 0
s = 0
while dist[cur] < 0 :
    dist[cur] = s 
    s += v[cur] - cur
    cur = v[cur] % N

# d1 - ループに入るまでの長さ, d2 - ループの長さ
d1 = dist[cur]
d2 = s - d1
NK = N * K

if NK > d1 :
    m = (NK-d1) % d2
    s = 0
    while m > dist[cur] :
        s = dist[cur]
        cur = v[cur] % N
    m -= s
else :
    m = 0
  
ret = []
last = dict()
for a in A[-m:] :
    if a in last and last[a] >= 0 :
        ret = ret[:last[a]]
        last[a] = -1
    else :
        ret.append(a)
        last[a] = len(ret)-1
        
print(' '.join([str(i) for i in ret]))

Submission status: Wrong Answer

Solution code:
N,K=map(int,input().split())
A=list(map(int,input().split()))
from collections import defaultdict
d=defaultdict(list)
for i,a in enumerate(A):
    d[a].append(i)
x=0
k=1
from bisect import bisect
while True:
    i=bisect(d[A[x]],x)
    if i==len(d[A[x]]):
        if k==K:
            break
        i=0
        k+=1
    x=d[A[x]][i]+1
    if x==N:
        if K%k==0:
            break
        K=K%k
        k=1
        x=0
t=[]
while x<N:
    i=bisect(d[A[x]],x)
    if i==len(d[A[x]]):
        t.append(A[x])
        x+=1
    else:
        x=d[A[x]][i]+1
        if x<N:
            t.append(A[x])
print(*t)