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 = list(map(int, input().split()))
A = list(map(int, input().split()))
 
M = [None]*(max(A)+1)
T = [None]*N
for i,a in enumerate(A):
    M[a] = i
 
for i,a in enumerate(A):
    T[M[a]]=(i+1)%N
    M[a]=i
 
ptr=0
ptr_head = [ptr]
while True:
    ptr_next = T[ptr]
    if ptr_next==0: break
    if ptr_next <= ptr+1: ptr_head.append(ptr_next)
    ptr = ptr_next
 
period = len(ptr_head)
if T[-1]==0: period+=1
 
if K % period==0:
    print()
    exit()
 
ret = []
ptr = ptr_head[K % period - 1]
while ptr<N:
    ptr_next = T[ptr]
    if ptr_next > ptr+1:
        ptr = ptr_next
    elif ptr_next==0 and ptr!=N-1:
        break
    else:
        ret.append(A[ptr])
        ptr+=1
 
print(' '.join(map(str, ret)))