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()))
hoge = [[]for i in range(200001)]
for i in range(N):
    hoge[A[i]].append(i)
NEXT = [-1]*N
for i in hoge:
    for j in range(-len(i),0):
        NEXT[i[j]] = i[j+1]
i = 1
p = 0
while i < K:
    #print(i,p)
    if NEXT[p] <= p:
        i += 1
    if NEXT[p] == N-1:
        i += 1
    p = (NEXT[p]+1)%N
    if p == 0:
        i = ((K-1)//(i-1))*(i-1)+1
while p < N:
    if NEXT[p] <= p:
        print(A[p],end = " ")
        p += 1
    else:
        p = NEXT[p]+1
print()