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

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

import bisect
import sys
MAX_INT = int(10e12)
MIN_INT = -MAX_INT
mod = 1000000007
sys.setrecursionlimit(1000000000)
def IL(): return list(map(int,input().split()))
def SL(): return input().split()
def I(): return int(sys.stdin.readline())
def S(): return input()

def tami(index):
  if index == N:
    ans.append(-1)
    return
  num = a[index]
  if len(data[num]) == 1:
    ans.append(index)
    tami(index+1)
  elif index == data[num][-1]:
    ans.append(index)
    tami(data[num][0]+1)
  else:
    tmp = bisect.bisect_left(data[num],index)
    #print(num,data[num],tmp)
    tami(data[num][tmp+1]+1)

N,K = IL()
a = IL()

data = [[] for i in range(200010)]
ans = []

for i in range(N):
  data[a[i]].append(i)

#print(data)

tami(0)

#print(ans)
#print(len(ans),K)
#print(K%len(ans))

if K%len(ans) == 0:
  print()
else:
  x = ans[K%len(ans)-1]
  d = []
  d.append(a[x])
  while x != N-1:
    x += 1
    if len(data[a[x]]) == 1:
      d.append(a[x])
    elif x == data[a[x]][-1]:
      d.append(a[x])
    else:
      tmp = bisect.bisect_left(data[a[x]],x)
      x = data[a[x]][tmp+1]

  print(" ".join(map(str,d)))

"""
for i in range(K):
  for j in range(N):
    if a[j] in data:
      num = data.index(a[j])
      data = data[:num]
    else:
      data.append(a[j])
  print(data)

11 10
1 2 3 0 4 5 6 0 4 5 6

11 10
3 1 4 1 5 9 2 6 5 3 5

10 10
1 4 8 3 5 4 2 3 4 6
"""