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=list(map(int,input().split()))

last=[-1]*(2*10**5+1)
nex=[-1]*n
prog=[0]*n

for i,a in enumerate(A*2):
    l=last[a]
    last[a]=i%n
    if nex[l]==-1 and l!=-1:
        nex[l]=(i+1)%n
        if i>=n or i+1==n:
            prog[l]=1
if nex[-1]==0:
    prog[-1]+=1

flag=False #いっぱいループ済か
stage=0
now=0
roop=[-1]*n
while True:
    if roop[now]!=-1 and flag==False:
        flag=True
        rr=stage-roop[now]
        stage=k-1-(k-1-stage)%rr
    if stage+prog[now]>=k:
        break
    roop[now]=stage
    stage+=prog[now]
    now=nex[now]

A=A[now:]+A if k-1-stage else A[now:]
check=[0]*(2*10**5+1)
stack=[]
for a in A:
    if check[a]:
        while check[a]:
            check[stack.pop()]=0
        continue
    stack.append(a)
    check[a]=1

print(*stack)
