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)

mi = lambda: map(int, input().split())
e = enumerate
n,k = mi()
m = (n+k).bit_length()
a = list(mi())
g = [None]*n

d = dict()
for i,x in e(a):
  d[x] = i
for i,x in e(a):
  g[d[x]] = ((i+1)%n,int(d[x]>=i)+int(i+1==n))
  d[x] = i
db = [g]
for _ in range(m):
  old = db[-1]
  new = [None]*n
  for i in range(n):
    p,q = old[i]
    r,s = old[p]
    new[i] = (r,q+s)
  db.append(new)
cur = 0
st = m
cs = 0
while st>=0:
  p,q = db[st][cur]
  if cs+q < k:
    cs += q
    cur = p
  else:
    st -= 1
    
q = list()
while cur < n:
  if g[cur][1] == 0:
    cur = g[cur][0]
  elif g[cur] == (0,1):
    break
  else:
    q.append(a[cur])
    cur += 1
  
print(' '.join(map(str,q)))