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
n,k=map(int,input().split())
A=[int(i) for i in input().split()]
AA=[0]*n
B=[2*n+1]*(2*(10**5)+1)
for i in reversed(range(n)):
  B[A[i]]=n+i+1
for i in reversed(range(n)):
  AA[i]=B[A[i]]-(i+1)
  B[A[i]]=i+1
count,index,inc=0,0,0
Chk=[0]*n
flag=False
while count<n*k:

  inc=AA[index]+1
  count+=inc  
  index=(index+inc)%n
  if Chk[index]!=0 or index==0:
    if flag==False:
      dd=count-Chk[index]
      count+=(((n*k)-count)//dd)*dd
      flag=True
  Chk[index]=count

count-=inc
index=(index+n-inc)%n

d=n*k-count
Ans1=A+A
Ans2=AA+AA
Ans=[]
i=index
while i<d+index:
  if i+Ans2[i]>=d+index:
    Ans.append(Ans1[i])
    i+=1
  else:
    i+=Ans2[i]+1
print(*Ans)
