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

X = A * 2

Nextcount = [-1] * (2 * (10**5+1))
Nextind = [-1]*N

for i,x in enumerate(X):
    if 0 <= Nextcount[x] < N:
        Nextind[Nextcount[x]] = i

    Nextcount[x] = i

Repeatcount=0
NOW = 0

Repeatcount+=Nextind[NOW]-NOW+1
NOW=(Nextind[NOW]+1)%N

while NOW!=0:
    Repeatcount+=Nextind[NOW]-NOW+1
    NOW=(Nextind[NOW]+1)%N
    

Rep=(N*K)%Repeatcount
NOW=0

while True:
    if Nextind[NOW]-NOW+1<Rep:
        Rep-=Nextind[NOW]-NOW+1
        NOW=(Nextind[NOW]+1)%N

    else:
        break
    
#print(Rep,NOW)

from collections import Counter
C=Counter()
s=[]
for i in range(Rep):
    if X[(NOW+i)%N] in C:
        while X[(NOW+i)%N] in C:
            po=s.pop()
            C[po]-=1
            if C[po]==0:
                del C[po]

    else:
        s.append(X[(NOW+i)%N])
        C[X[(NOW+i)%N]]+=1

    #print(s,C)

print(*s)
        
            

