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
inf = 10 ** 18
P = 10 ** 9 + 7

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

d_x = {}
for idx, Ai in enumerate(A):
    if str(Ai) not in d_x.keys():
        d_x[str(Ai)] = [idx]
    else:
        d_x[str(Ai)].append(idx)

tab_jump = [None] * N
for key in d_x.keys():
    for i in range(len(d_x[key]) - 1):
        tab_jump[d_x[key][i]] = d_x[key][i + 1]
    tab_jump[d_x[key][-1]] = d_x[key][0]

ans = []
pos = 0
while True:
    # print("#", pos)
    if pos >= N * K: break
    pos_src = pos % N
    pos_dst = tab_jump[pos_src]
    if pos_src < pos_dst:
        pos_nxt = pos + (pos_dst - pos_src) + 1
    else:
        pos_nxt = pos + (pos_dst - pos_src) + N + 1
    #
    if pos_nxt > N * K:
        ans.append(A[pos_src])
        pos += 1
    else:
        if pos_nxt % N == 0:
            K_iter = pos_nxt // N
            pos = N * ((K // K_iter) * K_iter)
        else:
            pos = pos_nxt

if len(ans) > 0:
    print(' '.join(map(str, ans)))