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 bisect

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

dic={}
for i in range(N):
    if A[i] not in dic:
        dic[A[i]]=[]
    dic[A[i]].append(i)

check={}
for ai in dic:
    check[ai]=0
    check[ai]=max(dic[ai])


front=[-1]
pos=0
visit=set([-1])
while True:
    val=A[pos]
    if pos>=check[val]:
        front.append(pos)
        if pos in visit:
            break
        else:
            visit.add(pos)
        pos=dic[val][0]+1
        if pos==N:
            front.append(-1)
            break
    else:
        index=bisect.bisect_right(dic[val],pos)
        pos=dic[val][index]+1
        if pos==N:
            front.append(-1)
            break
last=front[-1]
i=front.index(last)
period=len(front)-i-1
const=i
K-=const
K-=1
r=K%period
fff=front[r]
if fff!=-1:
    import heapq
    que=[]
    check={A[i]:0 for i in range(N)}
    index=0
    flag=True
    while N>index:
        if A[index]!=A[fff] and flag:
            index+=1
        elif A[index]==A[fff] and flag:
            index+=1
            flag=False
        else:
            if check[A[index]]==0:
                heapq.heappush(que,(-index,A[index]))
                check[A[index]]=1
                index+=1
            else:
                while True:
                    test,a=heapq.heappop(que)
                    check[a]=0
                    if a==A[index]:
                        break
                check[A[index]]=0
                index+=1
    que.sort(reverse=True)
    que=[que[i][1] for i in range(len(que))]
    print(*que)
else:
    import heapq
    que=[]
    check={A[i]:0 for i in range(N)}
    index=0
    while N>index:
        if check[A[index]]==0:
            heapq.heappush(que,(-index,A[index]))
            check[A[index]]=0
            check[A[index]]=1
            index+=1
        else:
            while True:
                test,a=heapq.heappop(que)
                check[a]=0
                if a==A[index]:
                    break
            check[A[index]]=0
            index+=1
    que.sort(reverse=True)
    que=[que[i][1] for i in range(len(que))]
    print(*que)