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.

Examples

Input

3 2
1 2 3


Output

2 3


Input

5 10
1 2 3 2 3


Output

3


Input

6 1000000000000
1 1 2 2 3 3


Output




Input

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


Output

9 2 6
from bisect import *
N,K=map(int,input().split())
A=list(map(int,input().split()))
siz=200814
Y=[[] for i in range(siz)]
p=[]
for i in range(N):
  Y[A[i]].append(i)
  p.append(i)
for i in range(N):
  Y[A[i]].append(N+i)
  p.append(i)
def f(x):
  S=set()
  r=[]
  for i in range(x,N):
    if A[i] in S:
      while True:
        S.discard(r[-1])
        if r[-1]==A[i]:
          del r[-1]
          break
        del r[-1]
    else:
      r.append(A[i])
      S.add(A[i])
  return r

Z=-1
R=0
V=0
while True:
  Z+=1
  V=Y[A[p[Z]]][bisect_right(Y[A[p[Z]]],Z)]
  if V>=N and R==K-1:
    print(*f(Z))
    exit()
  if V>=N:
    R+=1
    V=p[V]
  Z=V
  if Z==N-1:
    K%=(R+1)
    Z=-1
    R=0
    break
if K==0:
  print()
  exit()
while True:
  Z+=1
  V=Y[A[p[Z]]][bisect_right(Y[A[p[Z]]],Z)]
  if V>=N and R==K-1:
    print(*f(Z))
    exit()
  if V>=N:
    R+=1
    V=p[V]
  Z=V