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
import itertools
from bisect import bisect_left,bisect
import sys

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

A_max=max(A)
lst=[[] for i in range(A_max+1)]
flag=[0]*(A_max+1)
for i in range(n):
    lst[A[i]].append(i)

flag=[0]*n
data=[]
i=0
while flag[i]==0:
    flag[i]=1
    a=A[i]
    b=bisect(lst[a],i)
    if b==len(lst[a]):
        data.append(i)
        i=lst[a][0]+1
    else:
        i=lst[a][b]+1
    if i==n:
        data.append(n)
        i=0

#大丈夫
if not data:
    print()
    sys.exit()
s=len(data)
zzz=data[(K-1)%s]
i=zzz
d=[]
while i<n:
    a=A[i]
    b=bisect(lst[a],i)
    if b<len(lst[a]):
        d.append([i,lst[a][b]])
        i=lst[a][b]+1
        continue
    else:
        i+=1


if d:
    ans=A[zzz:d[0][0]]
    for j in range(len(d)-1):
        ans=list(itertools.chain(ans,A[d[j][1]+1:d[j+1][0]]))
    ans=list(itertools.chain(ans,A[d[-1][1]+1:]))
    print(*ans)
else:
    print(*A[zzz:])