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 sys
input=sys.stdin.readline
n,k=map(int,input().split())
a_list=list(map(int,input().split()))
dp=[-1]*(n+1)
dp[n]=0
D={}
for i in range(n-1,-1,-1):
    if not a_list[i] in D:
        dp[i]=a_list[i]
        D[a_list[i]]=i+1
    else:
        dp[i]=dp[D[a_list[i]]]
        D[a_list[i]]=i+1
first={}
for i in range(n):
    if not a_list[i] in first:
        first[a_list[i]]=i
cycle=[dp[0]]
i=dp[0]
while True:
    if i==0:
        break
    ne=first[i]
    i=dp[ne+1]
    cycle.append(i)
cycle.pop()
cycle=[0]+cycle
T=len(cycle)
order=k%T
if 1<=order:
    start=cycle[order-1]
    check={}
    if start==0:
        ans=[]
        for i in range(n):
            if ans==[]:
                ans.append(a_list[i])
                check[a_list[i]]=0
            else:
                if a_list[i] in check:
                    ans=ans[:check[a_list[i]]]
                    temp={}
                    for j in check:
                        if check[j]<check[a_list[i]]:
                            temp[j]=check[j]
                    check=temp
                else:
                    ans.append(a_list[i])
                    check[a_list[i]]=len(ans)-1
    else:
        ans=[]
        x=first[start]
        for i in range(x+1,n):
            if ans==[]:
                ans.append(a_list[i])
                check[a_list[i]]=0
            else:
                if a_list[i] in check:
                    ans=ans[:check[a_list[i]]]
                    temp={}
                    for j in check:
                        if check[j]<check[a_list[i]]:
                            temp[j]=check[j]
                    check=temp
                else:
                    ans.append(a_list[i])
                    check[a_list[i]]=len(ans)-1
    for i in ans:
        print(i,end='')
        print(' ',end='')
else:
    print()



    
